The Electronic Journal of Combinatorics
We show that, in a k-connected graph G of order n with α(G)=α, between any pair of vertices, there exists a path P joining them with
This implies that, for any edge e∈E(G), there is a cycle containing e of length at least
Moreover, we generalize our result as follows: for any choice S of s≤k vertices in G, there exists a tree T whose set of leaves is S with
Fujita, Shinya, Alexander Halperin, Colton Magnant.
"Long Path Lemma Concerning Connectivity and Independence Number."
The Electronic Journal of Combinatorics, 18 (1).