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
Partitionable graphs, circle graphs, and the berge strong perfect graph conjecture
β Scribed by Mark A. Buckingham; Martin Charles Golumbic
- Publisher
- Elsevier Science
- Year
- 1983
- Tongue
- English
- Weight
- 749 KB
- Volume
- 44
- Category
- Article
- ISSN
- 0012-365X
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
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
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
The chromatic number x of a graph G is the minimum number of colors necessary to color the vertices of G such that no two adjacent vertices are colored alike. The clique number 01 of a graph G is the maximum number of vertices in a complete subgraph of G. A graph G is said to be perfect if x(H) =m(H
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