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arXiv · 2309.13800

Enumerating All Maximal Clique-Partitions of an Undirected Graph

Mircea Marin·Temur Kutsia·Cleo Pau·Mikheil Rukhaia
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Abstract

We address the problem of enumerating all maximal clique-partitions of an undirected graph and present an algorithm based on the observation that every maximal clique-partition can be produced from the maximal clique-cover of the graph by assigning the vertices shared among maximal cliques, to belong to only one clique. This simple algorithm has the following drawbacks: (1) the search space is very large; (2) it finds some clique-partitions which are not maximal; and (3) some clique-partitions are found more than once. We propose two criteria to avoid these drawbacks. The outcome is an algorithm that explores a much smaller search space and guarantees that every maximal clique-partition is computed only once. The algorithm can be used in problems such as anti-unification with proximity relations or in resource allocation tasks when one looks for several alternative ways to allocate resources.

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Mircea Marin, Temur Kutsia, Cleo Pau, Mikheil Rukhaia. 2023-09-25. Enumerating All Maximal Clique-Partitions of an Undirected Graph. https://doi.org/10.4204/eptcs.389.6

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