Closure for {K1,4,K1,4 + e}-free graphs

Abstract

We introduce a closure concept for hamiltonicity in the class of {K1,4,K1,4+e}-free graphs, extending the closure for claw-free graphs introduced by Ryjáček (1997) [18]. The closure of a {K1,4,K1,4+e}-free graph G with minimum degree at least 6 is uniquely determined, is a line graph of a triangle-free graph, and preserves hamiltonicity or non-hamiltonicity of G. As applications, we show that many results on claw-free graphs can be directly extended to the class of {K1,4,K1,4+e}-free graphs.