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The Strong Perfect Graph Conjecture for Planar Graphs

Published online by Cambridge University Press:  20 November 2018

Alan Tucker
Alan Tucker*
Affiliation:
State University of New York, Stony Brook, New York
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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).

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 25 , Issue 1 , February 1973 , pp. 103 - 114
Copyright
Copyright © Canadian Mathematical Society 1973

References

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