Cliques and odd cycles are well known to induce facet-deΓΏning inequalities for the stable set polytope. In graph coloring cliques are a class of n-critical graphs whereas odd cycles represent the class of 3-critical graphs. In the ΓΏrst part of this paper we generalize both notions to (Kn \ e)-cycles
Gear composition and the stable set polytope
β Scribed by A. Galluccio; C. Gentile; P. Ventura
- Publisher
- Elsevier Science
- Year
- 2008
- Tongue
- English
- Weight
- 414 KB
- Volume
- 36
- Category
- Article
- ISSN
- 0167-6377
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β¦ Synopsis
We present a new graph composition that produces a graph G from a given graph H and a fixed graph B called gear and we study its polyhedral properties. This composition yields counterexamples to a conjecture on the facial structure of STAB(G) when G is claw-free.
π SIMILAR VOLUMES
Rank inequalities due to stability critical (u-critical) graphs are used to develop a finite nested sequence of linear relaxations of the stable set polytope, the strongest of which provides an integral max-min relation: In a simple graph, the maximum size of a stable set is equal to the minimum (we
In one of fundamental works in combinatorial optimization, Edmonds gave a complete linear description of the matching polytope. Matchings in a graph are equivalent to stable sets in its line graph. Also the neighborhood of any vertex in a line graph partitions into two cliques: graphs with this latt