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arXiv · 2003.03605

Clustering powers of sparse graphs

Jaroslav Nešetřil·Patrice Ossona de Mendez·Michał Pilipczuk·Xuding Zhu
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Abstract

We prove that if $G$ is a sparse graph --- it belongs to a fixed class of bounded expansion $\mathcal{C}$ --- and $d\in \mathbb{N}$ is fixed, then the $d$th power of $G$ can be partitioned into cliques so that contracting each of these clique to a single vertex again yields a sparse graph. This result has several graph-theoretic and algorithmic consequences for powers of sparse graphs, including bounds on their subchromatic number and efficient approximation algorithms for the chromatic number and the clique number.

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Jaroslav Nešetřil, Patrice Ossona de Mendez, Michał Pilipczuk, Xuding Zhu. 2020-03-07. Clustering powers of sparse graphs. https://arxiv.org/abs/2003.03605

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