Nonhamiltonian 2-connected claw-free graphs with large 4-degree sum

Wacław Frydrych
2001 Discrete Mathematics  
Let G be a 2-connected claw-free graph on n vertices. Let k (G) be the minimum degree sum among k-element independent set of vertices in G. It is proved that if 4(G)¿n + 3 then G is hamiltonian or else G belong to the known family of graphs. This is a generalization of the best known su cient condition on hamiltonicity in claw-free 2-connected graphs given independently by Liu, Zhang and Broersma. Moreover, it is shown that the problem HAMILTONIAN CYCLE restricted to claw-free graphs G = (V; E)
more » ... with 3(G)¿ 3 4 (|G| + 3) has polynomial time complexity. This contrasts sharply with known results on NP-completeness among dense graphs.
doi:10.1016/s0012-365x(00)00436-2 fatcat:waq752u2fzdgdfx4pvwm2xehuu