Every 3-connected $$\{K_{1,3},N_{1,2,3}\}$$ { K 1 , 3 , N 1 , 2 , 3 } -free graph is Hamilton-connected

Abstract

A graph G is $$\{X,Y\}$${X,Y}-free if it contains neither X nor Y as an induced subgraph. Pairs of connected graphs X, Y such that every 3-connected $$\{X,Y\}$${X,Y}-free graph is Hamilton-connected have been investigated recently in (2002, 2000, 2012). In this paper, it is shown that every 3-connected $$\{K_{1,3},N_{1,2,3}\}$${K1,3,N1,2,3}-free graph is Hamilton-connected, where $$N_{1,2,3}$$N1,2,3 is the graph obtained by identifying end vertices of three disjoint paths of lengths 1, 2, 3 to the vertices of a triangle.