Degree conditions restricted to induced paths for hamiltonicity of claw-heavy graphs

Abstract

Broersma and Veldman proved that every 2-connected claw-free and P 6 -free graph is hamiltonian. Chen et al. extended this result by proving every 2-connected clawheavy and P 6 -free graph is hamiltonian. On the other hand, Li et al. constructed a class of 2-connected graphs which are claw-heavy and P 6 -o-heavy but not hamiltonian.In this paper we further give some Ore-type degree conditions restricting to induced P 6 s of a 2-connected claw-heavy graph that can guarantee the graph to be hamiltonian. This improves some previous related results.

On implicit heavy subgraphs and Hamiltonicity of 2-connected graphs

“…Nevertheless, the condition of P6-o-heaviness can be replaced with other degree conditions on paths P6 to ensure Hamiltonicity of 2-connected claw-o-heavy graphs. We refer an interested reader to[24] for details.…”

Degree, toughness and subgraph conditions for hamiltonian properties of graphs

“…Nevertheless, the condition of P 6 -o-heaviness can be replaced with other degree conditions on paths P 6 to ensure hamiltonicity of 2-connected claw-o-heavy graphs. We refer the interested reader to[56] for details.…”