Get 20M+ Full-Text Papers For Less Than $1.50/day. Start a 14-Day Trial for You or Your Team.

Learn More →

Disjoint cliques in claw-free graphs

Disjoint cliques in claw-free graphs A graph is said to be claw-free if it does not contain an induced subgraph isomorphic to K 1,3. Let s and k be two integers with 0 ≤ s ≤ k and let G be a claw-free graph of order n. In this paper, we investigate clique partition problems in claw-free graphs. It is proved that if n ≥ 3s+4(k−s) and d(x)+d(y) ≥ n−2s+2k+1 for any pair of non-adjacent vertices x, y of G, then G contains s disjoint K 3s and k − s disjoint K 4s such that all of them are disjoint. Moreover, the degree condition is sharp in some cases. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Mathematicae Applicatae Sinica Springer Journals

Disjoint cliques in claw-free graphs

Loading next page...
 
/lp/springer-journals/disjoint-cliques-in-claw-free-graphs-YVX1CWIbva
Publisher
Springer Journals
Copyright
Copyright © 2018 by Institute of Applied Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences and Springer-Verlag GmbH Germany, part of Springer Nature
Subject
Mathematics; Applications of Mathematics; Math Applications in Computer Science; Theoretical, Mathematical and Computational Physics
ISSN
0168-9673
eISSN
1618-3932
DOI
10.1007/s10255-018-0737-y
Publisher site
See Article on Publisher Site

Abstract

A graph is said to be claw-free if it does not contain an induced subgraph isomorphic to K 1,3. Let s and k be two integers with 0 ≤ s ≤ k and let G be a claw-free graph of order n. In this paper, we investigate clique partition problems in claw-free graphs. It is proved that if n ≥ 3s+4(k−s) and d(x)+d(y) ≥ n−2s+2k+1 for any pair of non-adjacent vertices x, y of G, then G contains s disjoint K 3s and k − s disjoint K 4s such that all of them are disjoint. Moreover, the degree condition is sharp in some cases.

Journal

Acta Mathematicae Applicatae SinicaSpringer Journals

Published: Mar 8, 2018

References