Three-colourable perfect graphs without even pairs

Authors:
Maria Chudnovsky;Paul Seymour
Affiliations:
Columbia University, New York, NY 10027, United States;Princeton University, Princeton, NJ 08544, United States
Venue:
Journal of Combinatorial Theory Series B
Year:
2012

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Abstract

We still do not know how to construct the ''most general'' perfect graph, not even the most general three-colourable perfect graph. But constructing all perfect graphs with no even pairs seems easier, and here we make a start on it; we construct all three-connected three-colourable perfect graphs without even pairs and without clique cutsets. They are all either line graphs of bipartite graphs, or complements of such graphs.