Claw-free graphs with strongly perfect complements. Fractional and integral version. Part I. Basic graphs
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 0166-218XFull text not available from this repository.
Official URL: http://dx.doi.org/10.1016/j.dam.2011.06.024
Strongly perfect graphs have been studied by several authors (e.g. Berge and Duchet (1984) , Ravindra (1984)  and Wang (2006) ). 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)  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.|
|Page Range:||pp. 1971-1995|
|Access rights to Published version:||Restricted or Subscription Access|
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