منابع مشابه
Strong Perfect Graph Theorem
In 1960 Berge came up with the concept of perfect graphs, and in doing so, conjectured some characteristics about them. A perfect graph is a graph in which the chromatic number of every induced subgraph equals the size of the largest clique of that subgraph [2]. Two conjectures are now known as the Perfect Graph Theorem and the Strong Perfect Graph Theorem. Both of these theorems make deteminin...
متن کاملThe Strong Perfect Graph Theorem
A graph G is perfect if for every induced subgraph H, the chromatic number of H equals the size of the largest complete subgraph of H, and G is Berge if no induced subgraph of G is an odd cycle of length at least 5 or the complement of one. The “strong perfect graph conjecture” (Berge, 1961) asserts that a graph is perfect if and only if it is Berge. A stronger conjecture was made recently by C...
متن کاملThe Strong Perfect Graph Conjecture
A graph is perfect if, in all its induced subgraphs, the size of a largest clique is equal to the chromatic number. Examples of perfect graphs include bipartite graphs, line graphs of bipartite graphs and the complements of such graphs. These four classes of perfect graphs will be called basic. In 1960, Berge formulated two conjectures about perfect graphs, one stronger than the other. The weak...
متن کامل(k,r) - Semi Strong Chromatic Number of a Graph
Let G = (V, E) be a simple, finite, undirected graph. Let k, r be positive integers. A set S V (G) is called (k, r)-semi strongly stable set if | (u) S| k, for all u V (G). A partition of V(G) into (k, r)-semi strongly stable sets is called (k, r)-semi strong coloring of G. The minimum order of a (k, r)-semi strong coloring of G is called (k, r)-semi strong chromatic number of G and it is...
متن کاملForcing Colorations and the Strong Perfect Graph Conjecture
We give various reformulations of the Strong Perfect Graph Conjecture, based on a study of forced coloring procedures, uniquely colorable subgraphs and ! ? 1-cliques in minimal imperfect graphs.
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series B
سال: 1987
ISSN: 0095-8956
DOI: 10.1016/0095-8956(87)90022-0