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
A characterization of normal fraternally orientable perfect graphs
✍ Scribed by H. Galeana-Sánchez
- Publisher
- Elsevier Science
- Year
- 1997
- Tongue
- English
- Weight
- 255 KB
- Volume
- 169
- Category
- Article
- ISSN
- 0012-365X
No coin nor oath required. For personal study only.
✦ Synopsis
While the famous Berge's Strong Perfect Graph Conjecture remains a major unsolved problem in Graph Theory, the following alternative characterization of perfect graphs was conjectured in 1982 by C. Berge and P. Duchet: A graph G is perfect if and only if any normal orientation of G is kernel-perfect. In this paper I prove the validity of a version of this conjecture for graphs which accept a normal fraternal orientation.
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Let u(G) and i(G) be the domination number and independent domination number of a graph G. respectively. Sumner and Moore [8] define a graph G to be domination perfect if y( H) = i( H), for every induced subgraph H of G. In this article, we give a finite forbidden induced subgraph characterization o
## Abstract A b‐coloring is a coloring of the vertices of a graph such that each color class contains a vertex that has a neighbor in all other color classes, and the b‐chromatic number of a graph __G__ is the largest integer __k__ such that __G__ admits a b‐coloring with __k__ colors. A graph is b