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- 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 Sinica – Springer Journals
Published: Mar 8, 2018