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arXiv · 1804.00850

Boxicity, poset dimension, and excluded minors

Louis Esperet·Veit Wiechert
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Abstract

In this short note, we relate the boxicity of graphs (and the dimension of posets) with their generalized coloring parameters. In particular, together with known estimates, our results imply that any graph with no $K_t$-minor can be represented as the intersection of $O(t^2\log t)$ interval graphs (improving the previous bound of $O(t^4)$), and as the intersection of $\tfrac{15}2 t^2$ circular-arc graphs.

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Louis Esperet, Veit Wiechert. 2018-11-27. Boxicity, poset dimension, and excluded minors. https://arxiv.org/abs/1804.00850

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