English

Systolic inequalities and chromatic number

Combinatorics 2022-11-01 v1

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.

Keywords

Cite

@article{arxiv.2210.17090,
  title  = {Systolic inequalities and chromatic number},
  author = {Alexander Kamal and Roman Karasev},
  journal= {arXiv preprint arXiv:2210.17090},
  year   = {2022}
}

Comments

arXiv admin note: text overlap with arXiv:2106.10429