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Bull-Reducible Berge Graphs are Perfect

Hazel Everett 1 Celina de Figueiredo Sulamita Klein Bruce Reed
1 ISA - Models, algorithms and geometry for computer graphics and vision
INRIA Lorraine, LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
Abstract : Berge's well known SPGC (Strong Perfect Graph Conjecture) states that the class of perfect graphs coincides with the class of graphs containing no induced odd cycle of length at least 5 or the complement of such a cycle. A graph in this second class is called Berge. A bull is a graph with five vertices x, a, b, c, d and five edges xa, xb, ab, ad, bc. A graph is bull-reducible if no vertex is in two bulls. We prove that every bull-reducible Berge graph is perfect and we exhibit a polynomial-time recognition algorithm for bull-reducible Berge graphs.
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https://hal.inria.fr/inria-00100577
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Submitted on : Tuesday, September 26, 2006 - 2:47:48 PM
Last modification on : Friday, February 26, 2021 - 3:28:03 PM

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Hazel Everett, Celina de Figueiredo, Sulamita Klein, Bruce Reed. Bull-Reducible Berge Graphs are Perfect. Euroconference on Combinatorics, Graph Theory and Applications - COMB'01, 2001, Barcelone, Spain, 3 p. ⟨inria-00100577⟩

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