About the Strong Perfect Graph Conjecture on circular partitionable graphs
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On classes of minimal circular-imperfect graphs
Circular-perfect graphs form a natural superclass of perfect graphs: on the one hand due to their definition by means of a more general coloring concept, on the other hand as an important class of χ-bound graphs with the smallest non-trivial χ-binding function χ(G) ≤ ω(G) + 1. The Strong Perfect Graph Conjecture, recently settled by Chudnovsky et al. [4], provides a characterization of perfect ...
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Results of Lovász (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 Chvátal, Graham, Perold and Whitesides (1979). Results of Sebő (1996) entail that Berge’s conjecture holds for all the partitionable graphs obtained by this ...
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Results of Lovász and Padberg entail that the class of so-called partitionable graphs contains all the potential counterexamples to Berge’s famous Strong Perfect Graph Conjecture, which asserts that the only minimal imperfect graphs are the odd chordless cycles with at least five vertices (”odd holes”) and their complements (”odd antiholes”). Only two constructions (due to Chvátal, Graham, Pero...
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