Combinatorial algorithms for the maximum k-plex problem

Authors:
Benjamin Mcclosky;Illya V. Hicks
Affiliations:
Department of Computational and Applied Mathematics, Rice University, Houston, USA 77005-1892;Department of Computational and Applied Mathematics, Rice University, Houston, USA 77005-1892
Venue:
Journal of Combinatorial Optimization
Year:
2012

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Abstract

The maximum clique problem provides a classic framework for detecting cohesive subgraphs. However, this approach can fail to detect much of the cohesive structure in a graph. To address this issue, Seidman and Foster introduced k-plexes as a degree-based clique relaxation. More recently, Balasundaram et al. formulated the maximum k-plex problem as an integer program and designed a branch-and-cut algorithm. This paper derives a new upper bound on the cardinality of k-plexes and adapts combinatorial clique algorithms to find maximum k-plexes.