Degree Conditions Restricted to Induced Paths for Hamiltonicity of Claw-heavy Graphs  

作　　者：Bin Long LI Bo NING Sheng Gui ZHANG 

机构地区：[1]Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an 710072, P. R. China [2]European Centre of Excellence NTIS, 30614 Pilsen, Czech Republic [3]Center for Applied Mathematics, Tianjin University, Tianjin 300072, P. R. China

出　　处：《Acta Mathematica Sinica,English Series》2017年第2期301-310,共10页数学学报（英文版）

基　　金：Supported by NSFC(Grant No.11271300);the Natural Science Foundation of Shaanxi Province(Grant No.2016JQ1002);the Project NEXLIZ–CZ.1.07/2.3.00/30.0038

摘　　要：Broersma and Veldman proved that every 2-connected claw-free and P6-free graph is hamil- tonian. Chen et al. extended this result by proving every 2-connected claw-heavy and P6-free graph is hamiltonian. On the other hand, Li et al. constructed a class of 2-connected graphs which are claw-heavy and P6-o-heavy but not hamiltonian. In this paper, we further give some Ore-type degree conditions restricting to induced copies of P6 of a 2-connected claw-heavy graph that can guarantee the graph to be hamiltonian. This improves some previous related results.Broersma and Veldman proved that every 2-connected claw-free and P6-free graph is hamil- tonian. Chen et al. extended this result by proving every 2-connected claw-heavy and P6-free graph is hamiltonian. On the other hand, Li et al. constructed a class of 2-connected graphs which are claw-heavy and P6-o-heavy but not hamiltonian. In this paper, we further give some Ore-type degree conditions restricting to induced copies of P6 of a 2-connected claw-heavy graph that can guarantee the graph to be hamiltonian. This improves some previous related results.

关 键 词：Hamiltonian graph forbidden subgraph condition degree condition claw-heavy graph closure theory 

分 类 号：O157.5[理学—数学]