The strong perfect graph conjecture for toroifal graphs
β Scribed by Charles Grinstead
- Publisher
- Elsevier Science
- Year
- 1981
- Tongue
- English
- Weight
- 236 KB
- Volume
- 30
- Category
- Article
- ISSN
- 0095-8956
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The Strong Perfect Graph Conjecture states that a graph is perfect iff neither it nor its complement contains an odd chordless cycle of size greater than or equal to 5. In this article it is shown that many families of graphs are complete for this conjecture in the sense that the conjecture is true
A graph G is perfect if for every induced subgraph H of G the chromatic number x(H) equals the largest number w ( H ) of pairwise adjacent vertices in H. Berge's famous Strong Perfect Graph Conjecture asserts that a graph G is perfect if and only if neither G nor its complement C contains an odd cho
We introduce the class of graphs such that every induced subgraph possesses a vertex whose neighbourhood can be split into a clique and a stable set. We prove that this class satisfies Berge's strong perfect graph conjecture. This class contains several well-known classes of (perfect) graphs and is