Hamiltonicity in 3-connected claw-free graphs

Authors:
Hong-Jian Lai;Yehong Shao;Mingquan Zhan
Affiliations:
Department of Mathematics, West Virginia University, Morgantown, WV;Department of Mathematics, Ohio University Southern Campus, Ironton, OH;Department of Mathematics, Millersville University, Millersville, PA
Venue:
Journal of Combinatorial Theory Series B
Year:
2006

Citing 8
Cited 1

On a closure concept in claw-free graphs

Journal of Combinatorial Theory Series B
Eulerian subgraphs containing given vertices and hamiltonian line graphs

Discrete Mathematics
Clique covering and degree conditions for hamiltonicity in claw-free graphs

Discrete Mathematics
Hamiltonicity and minimum degree in 3-connected claw-free graphs

Journal of Combinatorial Theory Series B
A note on degree conditions for Hamiltonicity in 2-connected claw-free graphs

Discrete Mathematics - Algebraic and topological methods in graph theory
Eulerian subgraphs and Hamilton-connected line graphs

Discrete Applied Mathematics
Graph Theory With Applications

Graph Theory With Applications
Eulerian subgraphs in 3-edge-connected graphs and Hamiltonian line graphs

Journal of Graph Theory

Hamiltonian claw-free graphs involving minimum degrees

Discrete Applied Mathematics

Quantified Score

Hi-index	0.00

Visualization

Abstract

Kuipers and Veldman conjectured that any 3-connected claw-free graph with order v and minimum degree δ ≥ (v+6)/10 is Hamiltonian for v sufficiently large. In this paper, we prove that if H is a 3-connected claw-free graph with sufficiently large order v, and if δ (H) ≥ (v + 5)/10, then either H is Hamiltonian, or δ(H) = (v+5)/10 and the Ryjáček's closure cl(H) of H is the line graph of a graph obtained from the Petersen graph P10 by adding (v - 15)/10 pendant edges at each vertex of P10.