Cycles passing through k + 1 vertices in k‐connected graphs
Jun Fujisawa, Tomoki Yamashita · Journal of Graph Theory · 2008
Abstract In this article, we prove the following theorem. Let k ≥ 3 be an integer, G be a k‐connected graph with minimum degree d and X be a set of k + 1 vertices on a cycle. Then G has a cycle of length at least min {2d,|V(G)|} passing through X. This result gives the positive answer to the Question posed by Locke [8]. © 2008 Wiley Periodicals, Inc. J Graph Theory 58:179–190, 2008