华中师范大学胡智全教授学术报告11月5日上午

报告摘要：In this talk, we show some results on long cycles through given elements ina graph. In particular, we consider the following problem proposed by Locke and Zhangin [Graphs and Combinatorics 7 (1991) 265-269]: Let G be a k-connected graph withminimum degree d and X a set of m vertices on a cycle of G. For which values of mand k, with m > k≥2, must G have a cycle of length at least min{2d，|V (G)|}passingthrough X? Fujisawa and Yamashita solved this problem for the case k≥3 and m=k+1in [Journal of Graph Theory 58 (2008), 179-190]. We provide an affirmative answer tothis problem for the case of k≥3 and k+1≤m≤(4k+1)/3. This is a joint work withFeifei Song.