English

Positroids are 3-colorable

Combinatorics 2024-04-03 v4

Abstract

We show that every positroid of rank r3r \geq 3 has a good coline. Using the definition of the chromatic number of oriented matroid introduced by J.\ Ne\v{s}et\v{r}il, R.\ Nickel, and W.~Hochst\"{a}ttler, this shows that every orientation of a positroid is 3-colorable.

Cite

@article{arxiv.2111.06983,
  title  = {Positroids are 3-colorable},
  author = {Lamar Chidiac and Winfried Hochstättler},
  journal= {arXiv preprint arXiv:2111.06983},
  year   = {2024}
}
R2 v1 2026-06-24T07:36:56.802Z