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  • Combinatorics probability and computing

     Drmota, Michael; Llado Sanchez, Anna
    Combinatorics probability and computing
    Date of publication: 2014-01-06
    Journal article

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    We show that asymptotically almost surely a tree with m edges decomposes the complete bipartite graph K 2m,2m , a result connected to a conjecture of Graham and Häggkvist. The result also implies that asymptotically almost surely a tree with m edges decomposes the complete graph with O(m 2) edges. An ingredient of the proof consists in showing that the bipartition classes of the base tree of a random tree have roughly equal size.

  • On the second neighborhood conjecture of Seymour for regular digraphs with almost optimal connectivity

     Llado Sanchez, Anna
    European journal of combinatorics
    Date of publication: 2013-09-02
    Journal article

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  • On vosperian and superconnected vertex-transitive digraphs

     Hamidoune, Yahya O.; Llado Sanchez, Anna; López Masip, Susana Clara
    Graphs and combinatorics
    Date of publication: 2013
    Journal article

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  • On a conjecture of Graham and Häggkvist for random trees

     Drmota, Michael; Llado Sanchez, Anna
    European Conference on Combinatorics, Graph Theory and Applications
    Presentation's date: 2013-09-11
    Presentation of work at congresses

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  • Algunas conjeturas sobre descomposiciones de grafos

     Llado Sanchez, Anna
    Congreso de la Real Sociedad Española de Matemáticas
    Presentation's date: 2013-01-25
    Presentation of work at congresses

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  • Magic and antimagic H-decompositions

     Inayah, Nur; Llado Sanchez, Anna; Moragas Vilarnau, Jordi
    Discrete mathematics
    Date of publication: 2012-12-03
    Journal article

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    A decomposition of a graph G into isomorphic copies of a graph H is H-magic if there is a bijection f:V(G)¿E(G)¿0,1,...,|V(G)|+|E(G)|-1 such that the sum of labels of edges and vertices of each copy of H in the decomposition is constant. It is known that complete graphs do not admit K2-magic decompositions for n>6. By using the results on the sumset partition problem, we show that the complete graph K2 m+1 admits T-magic decompositions by any graceful tree with m edges. We address analogous problems for complete bipartite graphs and for antimagic and (a,d)-antimagic decompositions. © 2012 Elsevier B.V. All rights reserved.

  • On the modular sumset partition problem

     Llado Sanchez, Anna; Moragas Vilarnau, Jordi
    European journal of combinatorics
    Date of publication: 2012-04-28
    Journal article

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    A sequence m 1=m 2=¿;=m k of k positive integers isn-realizable if there is a partition X 1, X 2,..., X k of the integer interval [1, n] such that the sum of the elements in X i is m i for each i=1, 2,..., k. We consider the modular version of the problem and, by using the polynomial method by Alon (1999) [2], we prove that all sequences in Z/pZ of length k=(p-1)/2 are realizable for any prime p=3. The bound on k is best possible. An extension of this result is applied to give two results of p-realizable sequences in the integers. The first one is an extension, for n a prime, of the best known sufficient condition for n-realizability. The second one shows that, for n=(4k) 3, an n-feasible sequence of length k isn-realizable if and only if it does not contain forbidden subsequences of elements smaller than n, a natural obstruction forn-realizability. © 2011 Elsevier Ltd.

  • Optimización y problemas extremales en teoria de grafos y combinatoria. Aplicacions a les redes de comunicación

     Aguilo Gost, Francisco de Asis Luis; Abiad Monge, Aida; Andrés Yebra, José Luis; Barriere Figueroa, Eulalia; Cámara Vallejo, Marc; Ball, Simeon Michael; Comellas Padro, Francesc de Paula; Dalfo Simo, Cristina; Fàbrega Canudas, Josep; Garriga Valle, Ernest; Gomez Marti, Jose; Llado Sanchez, Anna; López Masip, Susana Clara; Miralles De La Asuncion, Alicia; Mitjana Riera, Margarida; Muñoz Lopez, Francisco Javier; Pelayo Melero, Ignacio Manuel; Pérez Mansilla, Sonia; Rius Font, Miquel; Serra Albo, Oriol; Vena, Lluis; Vilaltella Castanyer, Joan; Zaragoza Monroig, Maria Luisa; Espona Dones, Margarida; Sau Valls, Ignasi; Montejano Cantoral, Amanda; Perarnau Llobet, Guillem; Moragas Vilarnau, Jordi; Vena Cros, Lluís; Andres Yebra, Jose Luis; Fiol Mora, Miquel Àngel
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  • Yahya Ould Hamidoune, 1948--2011

     Llado Sanchez, Anna; Serra Albo, Oriol; Plagne, Alain
    Date: 2012-03-01
    Report

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  • Vertex-transitive graphs that remain connected after failure of a vertex and its neighbors

     Hamidoune, Yayha Old; Llado Sanchez, Anna; López Masip, Susana Clara
    Journal of graph theory
    Date of publication: 2011-12-05
    Journal article

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  • Vertex-transitive graphs that remain connected after failure of a vertex and its neighbors

     Hamidoune, Yayha Old; Llado Sanchez, Anna; López Masip, Susana Clara
    Journal of graph theory
    Date of publication: 2011-06
    Journal article

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    A d-regular graph is said to be superconnected if any disconnecting subset with cardinality at most d is formed by the neighbors of some vertex. A superconnected graph that remains connected after the failure of a vertex and its neighbors will be called vosperian. Let Γ be a vertex-transitive graph of degree d with order at least d+4. We give necessary and sufficient conditions for the vosperianity of Γ. Moreover, assuming that distinct vertices have distinct neighbors, we show that Γ is vosperian if and only if it is superconnected. Let G be a group and let S⊂G\{1} with S=S−1. We show that the Cayley graph, Cay(G, S), defined on G by S is vosperian if and only if G\(S∪{1}) is not a progression and for every non-trivial subgroup H and every a∈G, If moreover S is aperiodic, then Cay(G, S) is vosperian if and only if it is superconnected.

  • Almost every tree decomposes K2n,2n

     Llado Sanchez, Anna
    European Conference on Combinatorics, Graph Theory and Applications
    Presentation's date: 2011-09-06
    Presentation of work at congresses

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  • Every tree is a large subtree of a tree that decomposes Kn or Kn,n

     Llado Sanchez, Anna; López Masip, Susana Clara; Moragas Vilarnau, Jordi
    Discrete mathematics
    Date of publication: 2010-02-28
    Journal article

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    Let T be a tree with m edges. A well-known conjecture of Ringel states that T decomposes the complete graph $K_{2m+1}$. Graham and Häggkvist conjectured that T also decomposes the complete bipartite graph $K_{m,m}$. In this paper we show that there exists an integer n with n ≤[(3m - 1)/2] and a tree T₁ with n edges such that T₁ decomposes $K_{2n+1}$ and contains T. We also show that there exists an integer n' with n' ≥ 2m-1 and a tree T₂ with n' edges such that T₂ decomposes $K_{n',n'}$and contains T. In the latter case, we can improve the bound if there exists a prime p such that [3m/2] ≤ p < 2m - 1.

  • Graph labelings and decompositions by partitioning sets of integers  Open access

     Moragas Vilarnau, Jordi
    Defense's date: 2010-06-14
    Department of Applied Mathematics IV, Universitat Politècnica de Catalunya
    Theses

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    Aquest treball és una contribució a l'estudi de diferents problemes que sorgeixen de dues àrees fortament connexes de la Teoria de Grafs: etiquetaments i descomposicions. Molts etiquetaments de grafs deuen el seu origen als presentats l'any 1967 per Rosa. Un d'aquests etiquetaments, àmpliament conegut com a etiquetament graceful, va ser definit originalment com a eina per atacar la conjectura de Ringel, la qual diu que el graf complet d'ordre 2m+1 pot ser descompost en m copies d'un arbre donat de mida m. Aquí, estudiem etiquetaments relacionats que ens donen certes aproximacions a la conjectura de Ringel, així com també a una altra conjectura de Graham i Häggkvist que, en una forma dèbil, demana la descomposició d'un graf bipartit complet per un arbre donat de mida apropiada. Les principals contribucions que hem fet en aquest tema són la prova de la darrera conjectura per grafs bipartits complets del doble de mida essent descompostos per arbres de gran creixement i un nombre primer d'arestes, i la prova del fet que cada arbre és un subarbre gran de dos arbres pels quals les dues conjectures es compleixen respectivament. Aquests resultats estan principalment basats en una aplicació del mètode polinomial d'Alon. Un altre tipus d'etiquetaments, els etiquetaments magic, també són tractats aquí. Motivats per la noció de quadrats màgics de Teoria de Nombres, en aquest tipus d'etiquetaments volem asignar nombres enters a parts del graf (vèrtexs, arestes, o vèrtexs i arestes) de manera que la suma de les etiquetes assignades a certes subestructures del graf sigui constant. Desenvolupem tècniques basades en particions de certs conjunts d'enters amb algunes condicions additives per construir etiquetaments cycle-magic, un nou tipus d'etiquetament introduït en aquest treball i que estén la noció clàssica d'etiquetament magic. Els etiquetaments magic no donen cap descomposició de grafs, però les tècniques usades per obtenir-los estan al nucli d'un altre problema de descomposició, l'ascending subgraph decomposition (ASD). Alavi, Boals, Chartrand, Erdös i Oellerman, van conjecturar l'any 1987 que tot graf té un ASD. Aquí, estudiem l'ASD per grafs bipartits, una classe de grafs per la qual la conjectura encara no ha estat provada. Donem una condició necessària i una de suficient sobre la seqüència de graus d'un estable del graf bipartit de manera que admeti un ASD en que cada factor sigui un star forest. Les tècniques utilitzades estan basades en l'existència de branca-acoloriments en multigrafs bipartits. També tractem amb el sumset partition problem, motivat per la conjectura ASD, que demana una partició de [n] de manera que la suma dels elements de cada part sigui igual a un valor prescrit. Aquí donem la millor condició possible per la versió modular del problema que ens permet provar els millors resultats ja coneguts en el cas enter per n primer. La prova està de nou basada en el mètode polinomial.

    This work is a contribution to the study of various problems that arise from two strongly connected areas of the Graph Theory: graph labelings and graph decompositions. Most graph labelings trace their origins to the ones presented in 1967 by Rosa. One of these labelings, widely known as the graceful labeling, originated as a means of attacking the conjecture of Ringel, which states that the complete graph of order 2m+1 can be decomposed into m copies of a given tree of size m. Here, we study related labelings that give some approaches to Ringel's conjecture, as well as to another conjecture by Graham and Häggkvist that, in a weak form, asks for the decomposition of a complete bipartite graph by a given tree of appropriate size. Our main contributions in this topic are the proof of the latter conjecture for double sized complete bipartite graphs being decomposed by trees with large growth and prime number of edges, and the proof of the fact that every tree is a large subtree of two trees for which both conjectures hold respectively. These results are mainly based on a novel application of the so-called polynomial method by Alon. Another kind of labelings, the magic labelings, are also treated. Motivated by the notion of magic squares in Number Theory, in these type of labelings we want to assign integers to the parts of a graph (vertices, edges, or vertices and edges) in such a way that the sums of the labels assigned to certain substructures of the graph remain constant. We develop techniques based on partitions of certain sets of integers with some additive conditions to construct cycle-magic labelings, a new brand introduced in this work that extends the classical magic labelings. Magic labelings do not provide any graph decomposition, but the techniques that we use to obtain them are the core of another decomposition problem, the ascending subgraph decomposition (ASD). In 1987, was conjectured by Alavi, Boals. Chartrand, Erdös and Oellerman that every graph has an ASD. Here, we study ASD of bipartite graphs, a class of graphs for which the conjecture has not been shown to hold. We give a necessary and a sufficient condition on the one sided degree sequence of a bipartite graph in order that it admits an ASD by star forests. Here the techniques are based on the existence of edge-colorings in bipartite multigraphs. Motivated by the ASD conjecture we also deal with the sumset partition problem, which asks for a partition of [n] in such a way that the sum of the elements of each part is equal to a prescribed value. We give a best possible condition for the modular version of the sumset partition problem that allows us to prove the best known results in the integer case for n a prime. The proof is again based on the polynomial method.

  • On the ASD conjecture

     Llado Sanchez, Anna; Moragas Vilarnau, Jordi
    Jornadas de Matemática Discreta y Algorítmica
    Presentation's date: 2010-06-10
    Presentation of work at congresses

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    Let G be a graph of size ($\displaystyle\frac{n+1}{2}$) for some integer n ≥ 1. G is said to have an ascending subgraph decomposition (ASD) if can be decomposed into n subgraphs H1, . . . ,Hn such that Hi has i edges and is isomorphic to a subgraph of Hi+1, i = 1, . . . , n−1. In this work we deal with ascending subgraph decompositions of bipartite graphs. In order to do so, we consider ascending subgraph decompositions in which each factor is a forest of stars. We show that every bipartite graph G with($\displaystyle\frac{n+1}{2}$)edges such that the degree sequence d1 ≥ · · · ≥ dk of one of the partite sets satisfies d1 ≥ (k − 1)(n − k + 1), and di ≥ n − i + 2 for 2 ≤ i < k, admits an ASD with star forests. We also give a necessary condition on the degree sequence of G to have an ascending subgraph decomposition into star forests that is not far from the above sufficient one. Our results are based on the existence of certain matrices that we call ascending and the construction of edge-colorings of some bipartite graphs with parallel edges.

  • On the ascending subgraph decomposition problem for bipartite graphs

     Moragas Vilarnau, Jordi; Llado Sanchez, Anna
    Joint Mathematical Conference CSASC
    Presentation's date: 2010-01-26
    Presentation of work at congresses

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  • On the sumset partition problem

     Llado Sanchez, Anna; Moragas Vilarnau, Jordi
    French Combinatorial Conference
    Presentation's date: 2010-07-02
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  • On vosperian and superconnected arc-transitive digraphs

     Hamidoune, Yayha Old; Llado Sanchez, Anna; López Masip, Susana Clara
    International Workshop on Optimal Network Topologies
    Presentation's date: 2010-06-08
    Presentation of work at congresses

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  • On a conjecture of Graham and Haggkvist with the polynomial method

     Cámara Vallejo, Marc; Llado Sanchez, Anna; Moragas Vilarnau, Jordi
    European journal of combinatorics
    Date of publication: 2009-10
    Journal article

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  • COMBINATÒRIA , TEORIA DE GRAFS I APLICACIONS

     Comellas Padro, Francesc de Paula; López Masip, Susana Clara; Fiol Mora, Miquel Àngel; Garriga Valle, Ernest; Espona Dones, Margarida; Rius Font, Miquel; Aroca Farrerons, Josep Maria; Aguilo Gost, Francisco de Asis Luis; Dalfo Simo, Cristina; Moragas Vilarnau, Jordi; Cámara Vallejo, Marc; Gago Alvarez, Silvia; Ball, Simeon Michael; Andres Yebra, Jose Luis; Pérez Mansilla, Sonia; Mitjana Riera, Margarida; Llado Sanchez, Anna; Barriere Figueroa, Eulalia; Fàbrega Canudas, Josep; Muñoz Lopez, Francisco Javier; Zaragoza Monroig, Maria Luisa; Gomez Marti, Jose; Miralles De La Asuncion, Alicia; Pelayo Melero, Ignacio Manuel; Serra Albo, Oriol
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  • PROBLEMAS EXTREMALES Y DE OPTIMIZACIÓN EN TEORIA DE GRAFOS Y COMBINATORIA: APLICACIÓN AL ANALISIS Y ALGORITMOS DE REDES DE COMUNICAC

     Abiad Monge, Aida; Andres Yebra, Jose Luis; Aguilo Gost, Francisco de Asis Luis; Aroca Farrerons, Josep Maria; Ball, Simeon Michael; Barajas Tomas, Javier; Barguilla Navarrete, Jorge; Barriere Figueroa, Eulalia; Cámara Vallejo, Marc; Comellas Padro, Francesc de Paula; Dalfo Simo, Cristina; Espona Dones, Margarida; Fàbrega Canudas, Josep; Gago Alvarez, Silvia; Garriga Valle, Ernest; Gomez Marti, Jose; Llado Sanchez, Anna; López Masip, Susana Clara; Miralles De La Asuncion, Alicia; Mitjana Riera, Margarida; Montejano Cantoral, Amanda; Moragas Vilarnau, Jordi; Muñoz Lopez, Francisco Javier; Pelayo Melero, Ignacio Manuel; Perarnau Llobet, Guillem; Pérez Mansilla, Sonia; Rius Font, Miquel; Sau Valls, Ignasi; Serra Albo, Oriol; Vena, Lluis; Vilaltella Castanyer, Joan; Zaragoza Monroig, Maria Luisa; Vena Cros, Lluís; Fiol Mora, Miquel Àngel
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  • On the sumset partition problem

     Llado Sanchez, Anna; Moragas Vilarnau, Jordi
    European Conference on Combinatorics, Graph Theory and Applications
    Presentation's date: 2009-09
    Presentation of work at congresses

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  • On vosperian and superconnected vertex-transitive digraphs

     López Masip, Susana Clara; Hamidoune, Yayha Old; Llado Sanchez, Anna
    British Combinatorial Conference
    Presentation's date: 2009-07
    Presentation of work at congresses

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    Weinvestigatethestructureofadigraphhavingatransitiveautomorphism group where every cutset of minimal cardinality consists of all successors or all predecessors of some vertex. We give a complete characterization of vosperian arc-transitive digraphs. It states that an arc-transitive strongly connected digraph is vosperian if and only if it is irreducible. In particular, this is the case if the degree is coprime with the order of the digraph. We give also a complete characterization of vosperian Cayley digraphs and a complete characterization of irreducible superconnected Cayley digraphs. These two last characterizations extend the corresponding ones in Abelian Cayley digraphs and the ones in the undirected case.

  • On complete subsets of the cyclic group

     Hamidoune, Yahya O.; Llado Sanchez, Anna; Serra Albo, Oriol
    Journal of combinatorial theory. Series A
    Date of publication: 2008-10
    Journal article

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  • Invitación a la matemática discreta

     Matousek, Jirka; Jaroslav, Nesetril; Llado Sanchez, Anna
    Date of publication: 2008-06-30
    Book

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  • Chairman session

     Llado Sanchez, Anna
    Building Bridges
    Presentation's date: 2008-08-09
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  • Cyclic decompositions of K_n and K_n,n by a tree with a given large subtree

     Llado Sanchez, Anna; López Masip, Susana Clara; Moragas Vilarnau, Jordi
    Jornadas de Matemática Discreta y Algorítmica
    Presentation's date: 2008-07-22
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  • Cyclic decompositions of Kn and Kn,n by a tree with a given subtree

     Llado Sanchez, Anna; López Masip, Susana Clara
    Jornadas de Matemática Discreta y Algorítmica
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  • Cyclic decompositions of K_n by a given tree

     Llado Sanchez, Anna
    Jornadas de Matemática Discreta y Algorítmica
    Presentation's date: 2008-07-21
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  • Sumset Partition Problem

     Llado Sanchez, Anna
    Jornadas de Matemática Discreta y Algorítmica
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  • Sumset Partition Problem

     Llado Sanchez, Anna
    Jornadas de Matemática Discreta y Algorítmica
    Presentation's date: 2008-07-21
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  • Minisimposia Combstru

     Llado Sanchez, Anna
    European Congress of Mathematics
    Presentation's date: 2008-07-14
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  • Partición de un conjunto de enteros con sumas prescritas

     Llado Sanchez, Anna; Moragas Vilarnau, Jordi
    Jornadas de Matemática Discreta y Algorítmica
    Presentation's date: 2008-07
    Presentation of work at congresses

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  • On a Häggkvist's Conjecture with the Polynomial Method

     Cámara Vallejo, Marc; Llado Sanchez, Anna; Moragas Vilarnau, Jordi
    Electronic notes in discrete mathematics
    Date of publication: 2007-08
    Journal article

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  • Largest cliques in connected supermagic graphs

     Llado Sanchez, Anna
    European journal of combinatorics
    Date of publication: 2007-11
    Journal article

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  • Cycle-magic graphs

     Llado Sanchez, Anna; Moragas, J
    Discrete mathematics
    Date of publication: 2007-09
    Journal article

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    A simple graph G=(V,E) admits a cycle-covering if every edge in E belongs at least to one subgraph of G isomorphic to a given cycle C. Then the graph G is C-magic if there exists a total labelling f : V ∪ E → {1, 2, . . . , |V | + |E|} such that, for every subgraph H'=(V',E') of G isomorphic to C, $\Sigma_{v\in V'^{f{(v)}}}$ + $\Sigma{e \in E'}f^{(e)}$ is constant. When f(V)= {1, . . . , |V|}, then G is said to be C-supermagic. We study the cyclic-magic and cyclic-supermagic behavior of several classes of connected graphs. We give several families of Cr -magic graphs for each r≥3. The results rely on a technique of partitioning sets of integers with special properties.

  • On a H¨aggkvist¿s Conjecture with the Polynomial Method

     Llado Sanchez, Anna
    European Conference on Combinatorics, Graph Theory, and Applications
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  • Magic coverings

     Llado Sanchez, Anna
    Journal of combinatorial mathematics and combinatorial computing
    Date of publication: 2006-01
    Journal article

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  • Any tree is a large subgraph of a magic tree

     Llado Sanchez, Anna
    The australasian journal of combinatorics
    Date of publication: 2006-05
    Journal article

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  • Grafos H-magicos

     Llado Sanchez, Anna
    Jornadas de Matemática Discreta y Algorítmica
    Presentation's date: 2006-07-12
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  • Grafos H-mágicos

     Llado Sanchez, Anna; Moragas Vilarnau, Jordi
    Jornadas de Matemática Discreta y Algorítmica
    Presentation's date: 2006-07
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  • Edge-decompositions of K {n,n} into isomorphic copies of a given tree

     Llado Sanchez, Anna; López Masip, Susana Clara
    Journal of graph theory
    Date of publication: 2005-01
    Journal article

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  • Largest cliques in supermagic graphs

     Llado Sanchez, Anna
    Discrete mathematics and theoretical computer science
    Date of publication: 2005-09
    Journal article

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  • Minimum tree decompositions with a given tree as a factor

     Llado Sanchez, Anna; López Masip, Susana Clara
    The australasian journal of combinatorics
    Date of publication: 2005-02
    Journal article

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  • Combinatòria, Teoria de Grafs i Aplicacions

     Aguilo Gost, Francisco de Asis Luis; Serra Albo, Oriol; Andrés Yebra, José Luis; Balbuena Martinez, Maria Camino Teofila; Ball, Simeon Michael; Barajas Tomas, Javier; Barguilla Navarrete, Jorge; Barriere Figueroa, Eulalia; Comellas Padro, Francesc de Paula; Dalfo Simo, Cristina; Fàbrega Canudas, Josep; Fiol Mora, Miquel Àngel; Garriga Valle, Ernest; Gomez Marti, Jose; Llado Sanchez, Anna; López Masip, Susana Clara; Marcote Ordax, Francisco Javier; Miralles De La Asuncion, Alicia; Mitjana Riera, Margarida; Moragas Vilarnau, Jordi; Montejano Cantoral, Amanda; Muñoz Lopez, Francisco Javier; Pelayo Melero, Ignacio Manuel; Pérez Mansilla, Sonia; Rius Font, Miquel; Zaragoza Monroig, Maria Luisa
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  • Largest cliques in supermagic graphs

     Llado Sanchez, Anna
    European Conference on Combinatorics, Graph Theory and Applications
    Presentation's date: 2005-09-06
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  • Coverings and morphisms

     Llado Sanchez, Anna
    2nd Workshop on Morphisms on Graphs and applications
    Presentation's date: 2005-09-24
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  • Largest cliques in supermagic graphs

     Llado Sanchez, Anna
    European Conference on Combinatorics, Graph Theory and Applications
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  • Coverings and morphisms

     Llado Sanchez, Anna
    2nd Workshop on Morphisms on Graphs and applications
    Presentation's date: 2005-09-24
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  • Cycle-magic graphs

     Llado Sanchez, Anna; Moragas Vilarnau, Jordi
    International Workshop On Graph Labelings
    Presentation's date: 2005-07
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