Polar Permutation Graphs

Authors:
Tınaz Ekim;Pinar Heggernes;Daniel Meister
Affiliations:
Industrial Engineering Department, Boğaziçi University, Istanbul, Turkey;Department of Informatics, University of Bergen, Norway;Department of Informatics, University of Bergen, Norway
Venue:
Combinatorial Algorithms
Year:
2009

Citing 0
Cited 4

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ISAAC'11 Proceedings of the 22nd international conference on Algorithms and Computation
Polar permutation graphs are polynomial-time recognisable

European Journal of Combinatorics

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Abstract

Polar graphs generalise bipartite, cobipartite, split graphs, and they constitute a special type of matrix partitions. A graph is polar if its vertex set can be partitioned into two, such that one part induces a complete multipartite graph and the other part induces a disjoint union of complete graphs. Deciding whether a given arbitrary graph is polar, is an NP-complete problem. Here we show that for permutation graphs this problem can be solved in polynomial time. The result is surprising, as related problems like achromatic number and cochromatic number are NP-complete on permutation graphs. We give a polynomial-time algorithm for recognising graphs that are both permutation and polar. Prior to our result, polarity has been resolved only for chordal graphs and cographs.