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Critically partitionable graphs, I

✍ Scribed by A.G Thomason


Publisher
Elsevier Science
Year
1979
Tongue
English
Weight
268 KB
Volume
27
Category
Article
ISSN
0095-8956

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## Abstract Results of LovΓ‘sz (1972) and Padberg (1974) imply that partitionable graphs contain all the potential counterexamples to Berge's famous Strong Perfect Graph Conjecture. A recursive method of generating partitionable graphs was suggested by ChvΓ‘tal, Graham, Perold, and Whitesides (1979).

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Let ~1,22 ..... ~,; n/>2 be any properties of graphs. A vertex (~L, ~2 ..... J~,,)-partition of a graph G is a partition (V1, l~,...,/7,,) of V(G) such that for each i = 1,2 ..... n the induced subgraph G[Vi] has the property ~i. A graph G is said to be uniquely (~1,~2 ..... ~,)-partitionable if G h