A characterization of 2-connected {K1,3,N3,1,1}-free non-Hamiltonian graphs

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