On the Thomassen's conjecture*
Jianping Li · Journal of Graph Theory · 2001
Abstract C. Thomassen proposed a conjecture: Let G be a k‐connected graph with the stability number α ≥ k, then G has a cycle C containing k independent vertices and all their neighbors. In this paper, we will obtain the following result: Let G be a k‐connected graph with stability number α = k + 3 and C any longest cycle of G, then C contains k independent vertices and all their neighbors. This solves Thomassen's conjecture for the case α = k + 3. © 2001 John Wiley & Sons, Inc. J Graph Theory 37: 168–180, 2001