Distribution of Cycle Lengths in Graphs

Genghua Fan
2002 Journal of combinatorial theory. Series B (Print)  
Bondy and Vince proved that every graph with minimum degree at least three contains two cycles whose lengths differ by one or two, which answers a question raised by Erdő s. By a different approach, we show in this paper that if G is a graph with minimum degree d(G) \ 3k for any positive integer k, then G contains k+1 To settle a problem proposed by Bondy and Vince, we obtain that if G is a nonbipartite 3-connected graph with minimum degree at least 3k for any positive integer k, then G
more » ... 2k cycles of consecutive lengths m, m+1, ..., m+2k − 1 for some integer m \ k+2. © 2001 Elsevier Science (USA)
doi:10.1006/jctb.2001.2071 fatcat:ovmiwpya2ngbrm36ar33mauvxu