Finding a maximum-weight induced k-partite subgraph of an i-triangulated graph

Authors:
Louigi Addario-Berry;W. S. Kennedy;Andrew D. King;Zhentao Li;Bruce Reed
Affiliations:
School of Computer Science, McGill University, Montreal, Canada;School of Computer Science, McGill University, Montreal, Canada;School of Computer Science, McGill University, Montreal, Canada;School of Computer Science, McGill University, Montreal, Canada;School of Computer Science, McGill University, Montreal, Canada
Venue:
Discrete Applied Mathematics
Year:
2010

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Abstract

An i-triangulated graph is a graph in which every odd cycle has two non-crossing chords; i-triangulated graphs form a subfamily of perfect graphs. A slightly more general family of perfect graphs are clique-separable graphs. A graph is clique-separable precisely if every induced subgraph either has a clique cutset, or is a complete multipartite graph or a clique joined to an arbitrary bipartite graph. We exhibit a polynomial time algorithm for finding a maximum-weight induced k-partite subgraph of an i-triangulated graph, and show that the problem of finding a maximum-size bipartite induced subgraph in a clique-separable graph is NP-complete.