A characterization of 2-connected [formula omitted]-free non-Hamiltonian graphs

Abstract

In this paper, we characterize 2-connected {K1,3,N3,1,1}-free graphs without Hamiltonian cycle, where K1,3 is the star of order 4 and Nn1,n2,n3 is the graph obtained from K3 and three vertex-disjoint paths Pn1+1, Pn2+1, Pn3+1 by identifying each of vertices of K3 with an endvertex of one of the paths. Such a characterization gives some refinements for known results, for example, a characterization of 2-connected {K1,3,N3,1,1,N2,2,1}-free graphs containing no Hamiltonian cycle given in Brousek et al. (1999) and the existence of a 2-factor in 2-connected {K1,3,N3,1,1}-free graphs given in Faudree et al. (2008).