Abstract
Throughout this note, graph means finite, undirected graph without loops and multiple edges.
Communicated by W. T. Tuite
It is shown that a graph is perfect iff maximum clique . number of stability is not less than the number of vertices holds for each induced subgraph. The fact, conjectured by Berge and proved by the author, follows immediately that the complement of a perfect graph is perfect.
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References
C Berge, Färbung von Graphen, deren samtliche bzw deren ungerade Kreise Starr sind, Wiss Z Martin-Luther-Univ Halle-Wittenberg Math.-Natur Reihe(1961), 114.
D R Fulkerson, Blocking and anti-blocking pairs of polyhedra, 7th International Programming Symposium, The Hague, 1970.
L LovÁsz, Normal hypergraphs and the perfect graph conjecture, Discrete Math.,in press.
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LovÁsz, L. (2009). A Characterization of Perfect Graphs. In: Gessel, I., Rota, GC. (eds) Classic Papers in Combinatorics. Modern Birkhäuser Classics. Birkhäuser Boston. https://doi.org/10.1007/978-0-8176-4842-8_34
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