Fast Skew Partition Recognition

Authors:
William S. Kennedy;Bruce Reed
Affiliations:
Department of Mathematics and Statistics, McGill University, Montréal, Canada H3A2K6;School of Computer Science, McGill University, Montréal, Canada H3A2A7
Venue:
Computational Geometry and Graph Theory
Year:
2008

Citing 4
Cited 4

Some properties of minimal imperfect graphs

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Finding skew partitions efficiently

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Decomposing Berge graphs and detecting balanced skew partitions

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Skew partitions in perfect graphs

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The external constraint 4 nonempty part sandwich problem

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2K2-partition of some classes of graphs

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The P versus NP-complete dichotomy of some challenging problems in graph theory

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Graph partitions with prescribed patterns

European Journal of Combinatorics

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Abstract

Chvátal defined a skew partition of a graph G to be a partition of its vertex set into two non-empty parts A and B such that A induces a disconnected subgraph of G and B induces a disconnected subgraph of $\overline{G}$. Skew partitions are important in the characterization of perfect graphs. De Figuereido et al. presented a polynomial time algorithm which given a graph either finds a skew partition or determines that no such partition exists. It runs in O (n 101) time. We present an algorithm for the same problem which runs in O (n 4 m ) time.