Enumerating All Maximal Clique-Partitions of an Undirected Graph
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.
Keywords
Cite
@article{arxiv.2309.13800,
title = {Enumerating All Maximal Clique-Partitions of an Undirected Graph},
author = {Mircea Marin and Temur Kutsia and Cleo Pau and Mikheil Rukhaia},
journal= {arXiv preprint arXiv:2309.13800},
year = {2023}
}
Comments
In Proceedings FROM 2023, arXiv:2309.12959