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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
    p. 221-226
    Presentation's date: 2013-09-11
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  • Algunas conjeturas sobre descomposiciones de grafos

     Llado Sanchez, Anna
    Congreso de la Real Sociedad Española de Matemáticas
    p. 1
    Presentation's date: 2013-01-25
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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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  • 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; 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; Garriga Valle, Ernest; 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; Martí Farré, Jaume; Fiol Mora, Miquel Àngel
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  • Almost every tree decomposes K2n,2n

     Llado Sanchez, Anna
    European Conference on Combinatorics, Graph Theory and Applications
    p. 571-574
    DOI: 10.1016/j.endm.2011.09.093
    Presentation's date: 2011-09-06
    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 the ASD conjecture

     Llado Sanchez, Anna; Moragas Vilarnau, Jordi
    Jornadas de Matemática Discreta y Algorítmica
    p. 409-423
    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 vosperian and superconnected arc-transitive digraphs

     Hamidoune, Yayha Old; Llado Sanchez, Anna; López Masip, Susana Clara
    International Workshop on Optimal Network Topologies
    p. 143-150
    Presentation's date: 2010-06-08
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  • Graph labelings and decompositions by partitioning sets of integers  Open access

     Moragas Vilarnau, Jordi
    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 ascending subgraph decomposition problem for bipartite graphs

     Moragas Vilarnau, Jordi; Llado Sanchez, Anna
    Joint Mathematical Conference CSASC
    Presentation's date: 2010-01-26
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  • On the sumset partition problem

     Llado Sanchez, Anna; Moragas Vilarnau, Jordi
    European Conference on Combinatorics, Graph Theory and Applications
    p. 15-19
    Presentation's date: 2009-09
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  • COMBINATÒRIA , TEORIA DE GRAFS I APLICACIONS

     Rius Font, Miquel; Garriga Valle, Ernest; Cámara Vallejo, Marc; Espona Dones, Margarida; López Masip, Susana Clara; Comellas Padro, Francesc de Paula; Fiol Mora, Miquel Àngel; Moragas Vilarnau, Jordi; Fàbrega Canudas, Josep; Andres Yebra, Jose Luis; Ball, Simeon Michael; Gago Alvarez, Silvia; Dalfo Simo, Cristina; Miralles De La Asuncion, Alicia; Gomez Marti, Jose; Zaragoza Monroig, Maria Luisa; Barriere Figueroa, Eulalia; Llado Sanchez, Anna; Mitjana Riera, Margarida; Muñoz Lopez, Francisco Javier; Aguilo Gost, Francisco de Asis Luis; Pérez Mansilla, Sonia; Aroca Farrerons, Josep Maria; Pelayo Melero, Ignacio Manuel; Vena Cros, Lluís; Burillo Puig, Jose; Vilaltella Castanyer, Joan; Perarnau Llobet, Guillem; Serra Albo, Oriol
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  • On vosperian and superconnected vertex-transitive digraphs

     López Masip, Susana Clara; Hamidoune, Yayha Old; Llado Sanchez, Anna
    British Combinatorial Conference
    p. 21
    DOI: 10.1007/s00373-011-1104-4
    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.

  • 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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  • Chairman session

     Llado Sanchez, Anna
    Building Bridges
    Presentation's date: 2008-08-09
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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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  • 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
    p. 425-430
    Presentation's date: 2008-07-22
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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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  • 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
    p. 431-436
    Presentation's date: 2008-07
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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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  • Sumset Partition Problem

     Llado Sanchez, Anna
    Jornadas de Matemática Discreta y Algorítmica
    p. 431-437
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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
    p. 425-431
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  • On a H¨aggkvist¿s Conjecture with the Polynomial Method

     Llado Sanchez, Anna
    European Conference on Combinatorics, Graph Theory, and Applications
    p. 559-563
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  • Grafos H-magicos

     Llado Sanchez, Anna
    Jornadas de Matemática Discreta y Algorítmica
    p. 327-334
    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
    p. 327-334
    Presentation's date: 2006-07
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  • Combinatòria, Teoria de Grafs i Aplicacions

     Serra Albo, Oriol; Aguilo Gost, Francisco de Asis Luis; 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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  • 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
    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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  • Cycle-magic graphs

     Llado Sanchez, Anna; Moragas Vilarnau, Jordi
    International Workshop On Graph Labelings
    Presentation's date: 2005-07
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  • Largest cliques in supermagic graphs

     Llado Sanchez, Anna
    European Conference on Combinatorics, Graph Theory and Applications
    p. 212-222
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  • Magic coverings

     Llado Sanchez, Anna
    International Workshop on Graph Labeling
    Presentation's date: 2004-12-07
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  • Bigraceful labelings

     Llado Sanchez, Anna
    15th Australasian Workshop on Combinatorial Algorithms
    Presentation's date: 2004-07-07
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  • Combinatorica

     Llado Sanchez, Anna
    Collaboration in journals

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  • Bulletin of the Institute of Combinatorics and its Applications

     Llado Sanchez, Anna
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  • Evaluacion biomecanica del injerto anterior en cirugia del raquis lumbar. Estudio por elementos finitos

     Salo, G; Caceras, E; Lacroix, Damien Jerome; Mougolle, L; Planell Estany, Josep Antón; Molina, A; Llado Sanchez, Anna; Ramirez, M; Gracia, C
    XVIII Congreso Nacional de la Sociedad para el Estudio de las Enfermedades del Raquis
    p. 1
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  • The effect of spinal allograft on lumbar spine fusion: a finite element analysis

     Salo, G; Caceras, E; Lacroix, Damien Jerome; Mougolle, L; Planell Estany, Josep Antón; Molina, A; Llado Sanchez, Anna; Ramirez, M; Gracia, C
    SpineWeek 2004
    p. 681
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  • The australasian journal of combinatorics

     Llado Sanchez, Anna
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  • Combinatorics probability and computing

     Llado Sanchez, Anna
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  • Journal of combinatorial mathematics and combinatorial computing

     Llado Sanchez, Anna
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  • Graphs and combinatorics

     Llado Sanchez, Anna
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  • Minimum tree decompositions in simple graphs

     Llado Sanchez, Anna; López Masip, Susana Clara
    European conference on combinatorics, Graph theory and applications
    p. 255-258
    Presentation's date: 2003-09
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  • Labeling problems and Sidon sets

     Llado Sanchez, Anna
    European conference on combinatorics, Graph theory and applications
    Presentation's date: 2003-09-10
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  • DESCOMPOSICIONS DE GRAFS EN ARBRES.  Open access

     López Masip, Susana Clara
    Department of Applied Mathematics IV, Universitat Politècnica de Catalunya
    Theses

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  • Matemática discreta

     Comellas Padro, Francesc de Paula; Fàbrega Canudas, Josep; Llado Sanchez, Anna; Lladí, A S; Serra Albo, Oriol
    Date of publication: 2002-07-31
    Book

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  • Decompositions of graphs with a given tree

     Llado Sanchez, Anna; López Masip, Susana Clara
    Jornadas de Matemática Discreta y Algorítmica
    p. 204-211
    Presentation's date: 2002
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  • Magic graphs  Open access

     Muntaner Batle, Francesc Antoni
    Department of Applied Mathematics IV, Universitat Politècnica de Catalunya
    Theses

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    DE LA TESISSi un graf G admet un etiquetament super edge magic, aleshores G es diu que és un graf super edge màgic. La tesis està principalment enfocada a l'estudi del conjunt de grafs que admeten etiquetaments super edge magic així com també a desenvolupar relacions entre aquest tipus d'etiquetaments i altres etiquetaments molt estudiats com ara els etiquetaments graciosos i armònics, entre d'altres. De fet, els etiquetaments super edge magic serveixen com nexe d'unió entre diferents tipus d'etiquetaments, i per tant moltes relacions entre etiquetaments poden ser obtingudes d'aquesta forma. A la tesis també es proposa una nova manera de pensar en la ja famosa conjectura que afirma que tots els arbres admeten un etiquetament super edge magic. Això és, per a cada arbre T trobam un arbre super edge magic T' que conté a T com a subgraf, i l'ordre de T'no és massa gran quan el comparam amb l'ordre de T . Un problema de naturalesa similar al problema anterior, en el sentit que intentam trobar un graf super edge magic lo més petit possible i que contengui a cert tipus de grafs, i que ha estat completament resolt a la tesis es pot enunciar com segueix.Problema: Quin és un graf conexe G super edge magic d'ordre més petit que conté al graf complet Kn com a subgraf?.La solució d'aquest problema és prou interessant ja que relaciona els etiquetaments super edge magic amb un concepte clàssic de la teoria aditiva de nombres com són els conjunts de Sidon dèbils, també coneguts com well spread sets.De fet, aquesta no és la única vegada que el concepte de conjunt de Sidon apareix a la tesis. També quan a la tesis es tracta el tema de la deficiència , els conjunts de Sidon són d'una gran utilitat. La deficiencia super edge magic d'un graf és una manera de mesurar quan d'aprop està un graf de ser super edge magic. Tècnicament parlant, la deficiència super edge magic d'un graf G es defineix com el mínim número de vèrtexs aillats amb els que hem d'unirG perque el graf resultant sigui super edge magic. Si d'aquesta manera no aconseguim mai que el graf resultant sigui super edge magic, aleshores deim que la deficiència del graf és infinita. A la tesis, calculam la deficiència super edge magic de moltes families importants de grafs, i a més donam alguns resultats generals, sobre aquest concepte.Per acabar aquest document, simplement diré que al llarg de la tesis molts d'exemples que completen la tesis, i que fan la seva lectura més agradable i entenible han estat introduits.

    OF THESISIf a graph G admits a super edge magic labeling, then G is called a super edge magic graph. The thesis is mainly devoted to study the set of graphs which admit super edge magic labelings as well as to stablish and study relations with other well known labelings.For instance, graceful and harmonic labelings, among others, since many relations among labelings can be obtained using super edge magic labelings as the link.In the thesis we also provide a new approach to the already famous conjecture that claims that every tree is super edge magic. We attack this problem by finding for any given tree T a super edge magic tree T' that contains T as a subgraph, and the order of T'is not too large if we compare it with the order of T .A similar problem to this one, in the sense of finding small host super edge magic graphs for certain type of graphs, which is completely solved in the thesis, is the following one.Problem: Find the smallest order of a connected super edge magic graph G that contains the complete graph Kn as a subgraph.The solution of this problem has particular interest since it relates super edge magic labelings with the additive number theoretical concept of weak Sidon set, also known as well spread set. In fact , this is not the only time that this concept appears in the thesis.Also when studying the super edge magic deficiency, additive number theory and in particular well spread sets have proven to be very useful. The super edge magic deficiency of graph is a way of measuring how close is graph to be super edge magic.Properly speaking, the super edge magic deficiency of a graph G is defined to be the minimum number of isolated vertices that we have to union G with, so that the resulting graph is super edge magic. If no matter how many isolated vertices we union G with, the resulting graph is never super edge magic, then the super edge magic deficiency is defined to be infinity. In the thesis, we compute the super edge magic deficiency of may important families of graphs and we also provide some general results, involving this concept.Finally, and in order to bring this document to its end, I will just mention that many examples that improve the clarity of the thesis and makes it easy to read, can be found along the hole work.

  • Bulletin of the Institute of Combinatorics and its Applications

     Llado Sanchez, Anna
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  • Combinatorics probability and computing

     Llado Sanchez, Anna
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