The Strong Perfect Graph Conjecture for Planar Graphs
Canadian journal of mathematics, Tome 25 (1973) no. 1, pp. 103-114

Voir la notice de l'article provenant de la source Cambridge University Press

A graph G is called γ-perfect if ƛ (H) = γ(H) for every vertex-generated subgraph H of G. Here, ƛ(H) is the clique number of H (the size of the largest clique of H) and γ(H) is the chromatic number of H (the minimum number of independent sets of vertices that cover all vertices of H). A graph G is called α-perfect if α(H) = θ(H) for every vertex-generated subgraph H of G, where α (H) is the stability number of H (the size of the largest independent set of H) and θ(H) is the partition number of H (the minimum number of cliques that cover all vertices of H).
Tucker, Alan. The Strong Perfect Graph Conjecture for Planar Graphs. Canadian journal of mathematics, Tome 25 (1973) no. 1, pp. 103-114. doi: 10.4153/CJM-1973-009-3
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[l] l. Berge, C., Färbung von Graphen, derensämtlichebzw. derenungeradeKreisestarrsind, Wiss. Martin-Luther Univ. Halle-Wittenberg Math.-Natur. 1961. Google Scholar

[2] 2. Berge, C., Some classes of perfect graphs, in Graph theory and theoretical physics, Harary, F. (ed.) (Academic Press, New York, 1967). Google Scholar

[3] 3. Berge, C., The rank of a family of sets and some applications to graph theory, in Recent advances incombinatorics, Tutte, W. T. (ed.) (Academic Press, New York, 1969). Google Scholar

[4] 4. Fulkerson, D. R., The perfect graph conjecture and pluperfect graph theorem, in Second Chapel Hill Conference on combinatorial mathematics and its applications, Dowling, T. (éd.), (Chapel Hill, 1970). Google Scholar

[5] 5. Lovász, L., Normal hyper graphs and the perfect graph conjecture, Discrete Math. 2 (1972), 253–268. Google Scholar

[6] 6. Ore, O., The theory of graphs, AMS Colloquium Series, 1962. Google Scholar

[7] 7. Shannon, C. E., The zero-error capacity of a noisy channel, IRE Trans. Info. Thy.ITS (1956), 3. Google Scholar

[8] 8. Tucker, A. C., Perfect graphs and an application to optimizing municipal services, SIAM Rev., July (1973). Google Scholar

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