Circumferences of claw-free graphs (Q2721932)

Generalizing a theorem of \textit{F. Tian}, \textit{Z. Wu} and \textit{Y. Liu} [Some results on longest paths and cycles in \(K_{1,3}\)-free graphs, J. Changsha Railway Institute 4, No. 4, 105-106 (1986)] the authors claim that if \(G\) is a \(k\)-connected non-Hamiltonian claw-free graph, \(k\geq 2\), then the circumference of \(G\) is at least NEWLINE\[NEWLINE\min\Biggl\{\sum_{x\in X}d(x)+ 2k: X\text{ independent set of \(k\) vertices of \(G\)}\Biggr\}.NEWLINE\]