Hamiltonicity in claw-free graphs through induced bulls
A claw is the complete bipartite graph \(K_{1, 3}\) and a bull is the unique graph with the degree sequence 3, 3, 2, 1, 1. A graph \(G\) is claw- free if \(G\) contains no induced subgraph isomorphic to the claw. In this paper, the following conjecture proposed by \textit{H. Broersma} and \textit{H. J. Veldman} [Contemporary methods in graph theory. In honour of Prof. Dr. K. Wagner, 181-194 (1990; Zbl 0723.05082)] is proved: Let \(G\) be a 2- connected claw-free graph. Suppose that, for each induced bull \(B\) in \(G\), the degree one vertices of \(B\) have some common neighbor in \(G\). Then \(G\) contains a Hamilton cycle.
scientific article; zbMATH DE number 769311