Abstract.
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 c n contains a cycle of length t for every even t in the interval [4,e c(G) − K] and every odd t in the interval [K,o c(G) − K], where e c(G) and o c(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.
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Received: July 5, 2000 Final version received: April 17, 2002
2000 Mathematics Subject Classification. 05C38
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Gould, R., Haxell, P. & Scott, A. A Note on Cycle Lengths in Graphs. Graphs Comb 18, 491–498 (2002). https://doi.org/10.1007/s003730200035
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DOI: https://doi.org/10.1007/s003730200035