The Chvátal–Erdős condition for panconnectivity of triangle-free graphs Original Research Article

Let G be a triangle-free graph with n vertices whose independence number does not exceed its connectivity. In this paper, we prove if G is neither Kn/2,n/2 nor C5, then (i) every edge of G is contained in cycles of every length i for 4⩽i⩽n; (ii) any pair of distinct vertices of G is connected by paths of i vertices for any 5⩽i⩽n. This generalizes a recent result by Lou (Discrete Math. 152 (1996) 253).