Hamilton‐connected {claw,net}‐free graphs, II

Abstract

Abstract In the first one in this series of two papers, we have proved that every 3‐connected ‐free graph is Hamilton‐connected. In this paper, we continue in this direction by proving that every 3‐connected ‐free graph, where , is Hamilton‐connected (where is the graph obtained by attaching endvertices of three paths of lengths to a triangle). This together with a previous result of other authors completes the characterization of forbidden induced generalized nets implying Hamilton‐connectedness of a 3‐connected claw‐free graph. We also discuss remaining open cases in a full characterization of connected graphs such that every 3‐connected ‐free graph is Hamilton‐connected.