Claw-free graphs with strongly perfect complements. Fractional and integral version, Part II: Nontrivial strip-structures |
| |
Authors: | Maria Chudnovsky |
| |
Institution: | a Department of Industrial Engineering and Operations Research, Columbia University, New York, NY, USAb Université Paris Dauphine, Paris, Francec School of Computer Science, McGill University, Montreal, QC, Canada |
| |
Abstract: | Strongly perfect graphs have been studied by several authors (e.g., Berge and Duchet (1984) 1], Ravindra (1984) 7] and Wang (2006) 8]). In a series of two papers, the current paper being the second 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) 8] 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. |
| |
Keywords: | Claw-free graphs Forbidden induced subgraphs Strongly perfect graphs Wireless networking Structural graph theory |
本文献已被 ScienceDirect 等数据库收录! |
|