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arXiv · 2303.01997

Domination inequalities and dominating graphs

David Conlon·Joonkyung Lee
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Abstract

We say that a graph $H$ dominates another graph $H'$ if the number of homomorphisms from $H'$ to any graph $G$ is dominated, in an appropriate sense, by the number of homomorphisms from $H$ to $G$. We study the family of dominating graphs, those graphs with the property that they dominate all of their subgraphs. It has long been known that even-length paths are dominating in this sense and a result of Hatami implies that all weakly norming graphs are dominating. In a previous paper, we showed that every finite reflection group gives rise to a family of weakly norming, and hence dominating, graphs. Here we revisit this connection to show that there is a much broader class of dominating graphs.

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David Conlon, Joonkyung Lee. 2023-03-03. Domination inequalities and dominating graphs. https://doi.org/10.1017/s0305004124000185

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