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Claw-free graphs with strongly perfect complements. Fractional and integral version. Part I. Basic graphs
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Chudnovsky, Maria, Ries, Bernard and Zwols, Yori. (2011) Claw-free graphs with strongly perfect complements. Fractional and integral version. Part I. Basic graphs. Discrete Applied Mathematics, Vol.159 (No.17). pp. 1971-1995. ISSN 0166-218X
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Official URL: http://dx.doi.org/10.1016/j.dam.2011.06.024
Abstract
Strongly perfect graphs have been studied by several authors (e.g. Berge and Duchet (1984) [1], Ravindra (1984) [12] and Wang (2006) [14]). In a series of two papers, the current paper being the first one, we investigate a fractional relaxation of strong perfection. Motivated by a wireless networking problem, we consider claw-free graphs that are fractionally strongly perfect in the complement. We obtain a forbidden induced subgraph characterization and display graph-theoretic properties of such graphs. It turns out that the forbidden induced subgraphs that characterize claw-free graphs that are fractionally strongly perfect in the complement are precisely the cycle of length 6, all cycles of length at least 8, four particular graphs, and a collection of graphs that are constructed by taking two graphs, each a copy of one of three particular graphs, and joining them in a certain way by a path of arbitrary length. Wang (2006) [14] gave a characterization of strongly perfect claw-free graphs. As a corollary of the results in this paper, we obtain a characterization of claw-free graphs whose complements are strongly perfect. (C) 2011 Elsevier B.V. All rights reserved.
| Item Type: | Journal Article |
|---|---|
| Subjects: | Q Science > QA Mathematics |
| Divisions: | Faculty of Science > Mathematics |
| Journal or Publication Title: | Discrete Applied Mathematics |
| Publisher: | Elsevier Science Ltd. |
| ISSN: | 0166-218X |
| Date: | 2011 |
| Volume: | Vol.159 |
| Number: | No.17 |
| Page Range: | pp. 1971-1995 |
| Identification Number: | 10.1016/j.dam.2011.06.024 |
| Status: | Peer Reviewed |
| Publication Status: | Published |
| Access rights to Published version: | Restricted or Subscription Access |
| URI: | http://wrap.warwick.ac.uk/id/eprint/39613 |
Data sourced from Thomson Reuters' Web of Knowledge
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