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
On the strong perfect graph conjecture
✍ Scribed by V Chvátal
- Publisher
- Elsevier Science
- Year
- 1976
- Tongue
- English
- Weight
- 144 KB
- Volume
- 20
- Category
- Article
- ISSN
- 0095-8956
No coin nor oath required. For personal study only.
📜 SIMILAR VOLUMES
We will characterize all graphs that have the property that the graph and its complement are minimal even pair free. This characterization allows a new formulation of the Strong Perfect Graph Conjecture. The reader is assumed to be familiar with perfect graphs (see e.g. [2]). A hole is a cycle of l
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