RESEARCH ARTICLE

Disjoint K4- in claw-free graphs with minimum degree at least five

  • Yunshu GAO , 1 ,
  • Qingsong ZOU 2
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  • 1. School of Mathematics and Computer Science, Ningxia University, Yinchuan 750021, China
  • 2. Department of Mathematics, Xidian University, Xi’an 710071, China

Received date: 17 Mar 2012

Accepted date: 04 Oct 2014

Published date: 30 Dec 2014

Copyright

2014 Higher Education Press and Springer-Verlag Berlin Heidelberg

Abstract

A graph is said to be claw-free if it does not contain an induced subgraph isomorphic to K1,3. Let K4- be the graph obtained by removing exactly one edge from K4 and let k be an integer with k2. We prove that if G is a claw-free graph of order at least 13k - 12 and with minimum degree at least five, then G contains k vertex-disjoint copies of K4-. The requirement of number five is necessary.

Cite this article

Yunshu GAO , Qingsong ZOU . Disjoint K4- in claw-free graphs with minimum degree at least five[J]. Frontiers of Mathematics in China, 2015 , 10(1) : 53 -68 . DOI: 10.1007/s11464-014-0434-y

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