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Indexed by:期刊论文

Date of Publication:2013-07-01

Journal:DISCRETE APPLIED MATHEMATICS

Included Journals:SCIE、EI

Volume:161

Issue:10-11

Page Number:1530-1537

ISSN No.:0166-218X

Key Words:Claw-free graph; Cycle; 3-connectedness; Minimum degree

Abstract:Favaron and Fraisse proved that any 3-connected claw-free graph H with order n and minimum degree delta(H) >= n+38/10 is hamiltonian [O. Favaron and P. Fraisse, Hamiltonicity and minimum degree in 3-connected claw-free graphs, J. Combin. Theory B 82 (2001) 297-305]. Lai, Shao and Zhan showed that if H is a 3-connected claw-free graph of order n >= 196, and if delta(H) >= n+6/10, then H is hamiltonian [H.-J. Lai, Y. Shao and M. Zhan, Hamiltonicity in 3-connected claw-free graphs, J. Combin. Theory B 96 (2006) 493-504]. In this paper, we improve the two results above and prove that if H is a 3-connected claw-free graph of order n >= 363, and if delta(H) >= n+34/12, then either H is hamiltonian, or the Ryjacek's closure cl(H) of H is the line graph of one of the graphs obtained from the Petersen graph P-10 by adding at least one pendant edge at each vertex v(i) of P-10 or by replacing exactly one vertex v(i) of P-10 with (K) over bar (2,p) (p >= 2) and adding at least one pendant edge at all other nine vertices v(j) is not an element of V - {v(i)} of P-10, and then by subdividing m edges of P-10 for m = 0,1,2, ..., 15, where (K) over bar (2,p) connected bipartite graph. (C) 2013 Elsevier B.V. All rights reserved.