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On the order of graphs with a given girth pair

Autor
Balbuena, C.; Salas, J.
Tipus d'activitat
Article en revista
Revista
Discrete mathematics
Data de publicació
2014-04-28
Volum
321
Pàgina inicial
68
Pàgina final
75
DOI
https://doi.org/10.1016/j.disc.2013.12.015 Obrir en finestra nova
Projecte finançador
Control de invariantes en grafos sujetos a propiedades estructurales
URL
http://www.sciencedirect.com/science/article/pii/S0012365X13005268 Obrir en finestra nova
Resum
A (k; g, h)-graph is a k-regular graph of girth pair (g, h) where g is the girth of the graph, h is the length of a smallest cycle of different parity than g and g < h. A (k; g, h)-cage is a (k; g, h)-graph with the least possible number of vertices denoted by n(k; g, h). In this paper we give a lower bound on n(k; g, h) and as a consequence we establish that every (k; 6)-cage is bipartite if it is free of odd cycles of length at most 2k - 1. This is a contribution to the conjecture claiming tha...
Paraules clau
CAGES, Cages, Excess, Girth pair, REGULAR GRAPHS
Grup de recerca
COMBGRAPH - Combinatòria, Teoria de Grafs i Aplicacions

Participants