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arXiv · 2210.17090

Systolic inequalities and chromatic number

Alexander Kamal·Roman Karasev
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Abstract

We show that the discrete versions of the systolic inequality that estimate the number of vertices of a simplicial complex from below have substantial applications to graphs, the one-dimensional simplicial complexes. Almost directly they provide good estimates for the number of vertices of a graph in terms of its chromatic number and the length of the smallest odd cycle. Combined with the graph-theoretic techniques of Berlov and Bogdanov, the systolic approach produces even better estimates.

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Alexander Kamal, Roman Karasev. 2022-10-31. Systolic inequalities and chromatic number. https://arxiv.org/abs/2210.17090

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