Large degree vertices in longest cycles of graphs, II

Binlong Li (Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an, Shaanxi 710072, P.R. China)
Liming Xiong (School of Mathematics and Statistics, and Beijing Key Laboratory on MCAACI, Beijing Institute of Technology, Beijing, 100081, P.R. China)
Jun Yin (School of Computer Science, Qinghai Normal University, Xining, 810008, P.R. China)

Electronic Journal of Graph Theory and Applications (EJGTA)
Vol 7, No 2 (2019): Electronic Journal of Graph Theory and Applications

In this paper, we consider the least integer d such that every k-connected graph G of order n (and of independent number α) has a longest cycle containing all vertices of degree at least d. We completely determine the d when k = 2. We propose a conjecture for those k-connected graph, where k ≥ 3.