Circumferences and minimum degrees in 3-connected claw-free graphs

doi:10.1016/j.disc.2007.12.062

Discrete Mathematics

Volume 309, Issue 11, 6 June 2009, Pages 3580-3587

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Abstract

In this paper, we prove that every 3-connected claw-free graph $G$ on $n$ vertices contains a cycle of length at least min ${n, 6 δ - 15}$ , thereby generalizing several known results.

Keywords

Claw-free graph

Circumference

3-connectedness

Minimum degree

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^☆: Supported by the Natural Science Foundation of China under grant No. 60673046 and 90715037 (M. Li) and 10671014 (L. Xiong), by the Natural Science Foundation Project of Chongqing, CSTC under grant No. 2007BA2024 (M. Li) and by the Excellent Young Scholars Research Fund of Beijing Institute of Technology (No. 000Y07-28) (L. Xiong).

Discrete Mathematics

Circumferences and minimum degrees in 3-connected claw-free graphs☆

Abstract

Keywords