Abstract
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 of the order of a (k;g+1)-cage in terms of the order of a (k;g)-cage, improving a previous result by Sauer of 1967. We also show that every (k;11)-cage with k≥6 contains a cycle of length 12, supporting a conjecture by Harary and Kovács of 1983.
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