A note on the upper bound and girth pair of (k;g)-cages
作者： C. Balbuena , D. González-Moreno , J.J. Montellano-Ballesteros
DOI: 10.1016/J.DAM.2012.10.008
关键词: Mathematics 、 Upper and lower bounds 、 Graph 、 Combinatorics 、 Conjecture 、 Discrete mathematics 、 Cage
摘要: A (k;g)-cage is a k-regular graph of girth g with minimum order. In this work, for all k>=3 and g>=5 odd, we present an upper bound the order (k;g+1)-cage in terms (k;g)-cage, improving previous result by Sauer 1967. We also show that every (k;11)-cage k>=6 contains cycle length 12, supporting conjecture Harary Kovacs 1983.
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