English

Answers to some problems about graph coloring test graphs

Combinatorics 2017-08-01 v2 Algebraic Topology

Abstract

We prove that a graph whose chromatic number is 2 is a homotopy test graph. We also prove that there is a graph KK with two involutions γ1\gamma_1 and γ2\gamma_2 such that (K,γ1)(K,\gamma_1) is a Stiefel-Whitney test graph, but (K,γ2)(K,\gamma_2) is not. These are answers to some of the problems suggested by Kozlov.

Keywords

Cite

@article{arxiv.1303.1277,
  title  = {Answers to some problems about graph coloring test graphs},
  author = {Takahiro Matsushita},
  journal= {arXiv preprint arXiv:1303.1277},
  year   = {2017}
}

Comments

7 pages, 3 figures, final version. In the previous version, I actually solved a problem weaker than the original one

R2 v1 2026-06-21T23:37:24.053Z