Abstract
The chromatic number χ 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 ω 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 χ( H)= ω( H) for every induced subgraph H of G. Berge's strong perfect-graph conjecture states that G is perfect iff G does not contain C 2 n+1 and C ̄ 2n+1 , n⩾2 as an induced subgraph. In this paper we show that this conjecture is true for graphs which accept an orientation such that every complete subgraph has an absorbing vertex and the set of predecessors (resp: successors) of each vertex induces a complete subgraph. Also we obtain an equivalent version of the Strong Perfect Graph Conjecture.
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