The stable set polytope of claw-free graphs with stability number at least four. I. Fuzzy antihat graphs are W-perfect

被引：7
|
作者：
Galluccio, A. [1 ]
Gentile, C. [1 ]
Ventura, P. [1 ]
机构：
[1] CNR, Ist Anal Sistemi & Informat A Ruberti, IASI, I-00185 Rome, Italy
来源：
JOURNAL OF COMBINATORIAL THEORY SERIES B | 2014年 / 107卷
关键词：
Polyhedral combinatorics; Stable set polytope; Claw-free graphs; QUASI-LINE GRAPHS; POLYHEDRA;
D O I：
10.1016/j.jctb.2014.02.006
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Fuzzy antihat graphs are graphs obtained as 2-clique-bond compositions of fuzzy line graphs with three different types of three-cliqued graphs. By the decomposition theorem of Chudnovsky and Seymour [2], fuzzy antihat graphs form a large subclass of claw-free, not quasi-line graphs with stability number at least four and with no 1-joins. A graph is W-perfect if its stable set polytope is described by: nonnegativity, rank, and lifted 5-wheel inequalities. By exploiting the polyhedral properties of the 2-clique-bond composition, we prove that fuzzy antihat graphs are W-perfect and we move a crucial step towards the solution of the longstanding open question of finding an explicit linear description of the stable set polytope of claw-free graphs. (C) 2014 Elsevier Inc. All rights reserved.
引用
收藏
页码：92 / 122
页数：31
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