A degree sum condition for longest cycles in 3‐connected graphs
Tomoki Yamashita · Journal of Graph Theory · 2006
Abstract For a graph G, we denote by dG(x) and κ(G) the degree of a vertex x in G and the connectivity of G, respectively. In this article, we show that if G is a 3‐connected graph of order n such that dG(x) + dG(y) + dG(z) ≥ d for every independent set {x, y, z}, then G contains a cycle of length at least min{d − κ(G), n}. © 2006 Wiley Periodicals, Inc. J Graph Theory 54: 277–283, 2007