Hamilton connectivity of line graphs and claw-free graphs

  • Authors:

  • Zhiquan Hu;Feng Tian;Bing Wei

  • Affiliations:

  • Fac. of Math. and Stats. Central China Normal Univ. Wuhan Hubei 430079, People's Republic of China and Inst. of Sys. Sci. Acad. of Math. and Sys. Sci. Ch. Acad. of Sci. Beijing 100080, PRC;Institute of Systems Science Academy of Mathematics and Systems Sciences Chinese Academy of Sciences Beijing 100080, People's Republic of China;Institute of Systems Science Academy of Mathematics and Systems Sciences Chinese Academy of Sciences Beijing 100080, People's Republic of China and Department of Mathematics The University of Miss ...

  • Venue:
  • Journal of Graph Theory
  • Year:
  • 2005

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Abstract

Let G be a graph and let V0 ={νε V(G):dG(ν) = 6}. We show in this paper that:(i) if G is a 6-connected line graph and if|V0| ≤ 29 or G[V0]contains at most 5 vertex disjoint K4's, thenG is Hamilton-connected; (ii) every 8-connected claw-freegraph is Hamilton-connected. Several related results known beforeare generalized. © 2005 Wiley Periodicals, Inc. J GraphTheory