CYCLES IN TRIANGLE-FREE GRAPHS
Xiaojuan Li, Bing Wei, Yongjin Zhu · Discrete Mathematics Algorithms and Applications · 2011
Let G be a k-connected (k ≥ 3), triangle-free graph with α(G) ≤ k + 1. If G is not Petersen graph and G ∉ {Kk, k, Kk, k + 1, Kk + 1, k+1}, then G contains cycles of lengths from 4 to |V(G)|. This generalizes a result conjectured by Amar et al. (Graphs Combin.7 (1991)) and proved by Lou (Discrete Math.152 (1996)).