A Note on Cycle Lengths in Graphs

We prove that for every c > 0 there exists a constant K = K(c) such that every graph G with n vertices and minimum degree at least cn contains a cycle of length t for every even t in the interval [4, ec(G)-K] and every odd t in the interval [K, oc(G)-K], where ec(G) and oc(G) denote the length of the longest even cycle in G and the longest odd cycle in G respectively. We also give a rough estimate of the magnitude of K.

• Type: Journal
• Year: 2002
• Where: GC
• Authors: Ronald J. Gould, Penny E. Haxell, A. D. Scott
• Keywords: Applied Computing, GC 2002, Minimum Degree, Rough Estimate