Dominance complexes and vertex cover numbers of graphs

Takahiro Matsushita

Dominance complexes and vertex cover numbers of graphs

Combinatorics 2022-12-06 v2 Algebraic Topology

Authors: Takahiro Matsushita

Abstract

The dominance complex $D(G)$ of a simple graph $G = (V,E)$ is the simplicial complex consisting of the subsets of $V$ whose complements are dominating. We show that the connectivity of $D(G)$ plus $2$ is a lower bound for the vertex cover number $\tau(G)$ of $G$ .

Keywords

dominance complex simple graph simplicial complex dominating set connectivity vertex cover number

Cite

@article{arxiv.2009.04145,
  title  = {Dominance complexes and vertex cover numbers of graphs},
  author = {Takahiro Matsushita},
  journal= {arXiv preprint arXiv:2009.04145},
  year   = {2022}
}

Comments

6 pages, the title was slightly modified, final version, to appear in Journal of Applied and Computational Topology

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