Let S be an arbitrary collection of stars in a graph G such that there is no chain of length ~3 joining the centers of (any) two stars in G. We consider the graphs that can be obtained by deleting in a parity graph all the edges of such a set S. These graphs will be called skeletal graphs and we pro
New classes of Berge perfect graphs
โ Scribed by C. De Simone; A. Galluccio
- Publisher
- Elsevier Science
- Year
- 1994
- Tongue
- English
- Weight
- 823 KB
- Volume
- 131
- Category
- Article
- ISSN
- 0012-365X
No coin nor oath required. For personal study only.
โฆ Synopsis
In this paper we prove the validity of the Strong Perfect Graph Conjecture for some classes of graphs described by forbidden configurations.
Three different kinds of techniques are used: the first is the well-known star-cutset technique, the second involves a clique-reduction operation, and the third is based on a new equivalence of the Strong Perfect Graph Conjecture.
๐ SIMILAR VOLUMES
Let ฮฑ(G), ฮณ(G), and i(G) be the independence number, the domination number, and the independent domination number of a graph G, respectively. For any k โฅ 0, we define the following hereditary classes: ฮฑi where ISub(G) is the set of all induced subgraphs of a graph G. In this article, we present a f
Chilakamarri, K.B. and P. Hamburger, On a class of kernel-perfect and kernel-perfect-critical graphs, Discrete Mathematics 118 (1993) 253-257. In this note we present a construction of a class of graphs in which each of the graphs is either kernel-perfect or kernel-perfect-critical. These graphs or