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A note on the upper bound and girth pair of (k; g)-cages

Autor
Balbuena, C.; González, D.; Montellano-Ballesteros, J.J.
Tipus d'activitat
Article en revista
Revista
Discrete applied mathematics
Data de publicació
2013-04
Volum
161
Número
6
Pàgina inicial
853
Pàgina final
857
DOI
https://doi.org/10.1016/j.dam.2012.10.008 Obrir en finestra nova
Resum
A (k;g)(k;g)-cage is a kk-regular graph of girth gg with minimum order. In this work, for all k=3k=3 and g=5g=5 odd, we present an upper bound of the order of a (k;g+1)(k;g+1)-cage in terms of the order of a (k;g)(k;g)-cage, improving a previous result by Sauer of 1967. We also show that every (k;11)(k;11)-cage with k=6k=6 contains a cycle of length 12, supporting a conjecture by Harary and Kovács of 1983.
Paraules clau
Cage, Girth pair, Kronecker product
Grup de recerca
COMBGRAPH - Combinatòria, Teoria de Grafs i Aplicacions

Participants