Hedetniemi's conjecture is asymptotically false

Xiaoyu He; Yuval Wigderson

doi:10.1016/j.jctb.2020.03.003

paper

Hedetniemi's conjecture is asymptotically false

arXiv:1906.06783 · doi:10.1016/j.jctb.2020.03.003

Abstract

Extending a recent breakthrough of Shitov, we prove that the chromatic number of the tensor product of two graphs can be a constant factor smaller than the minimum chromatic number of the two graphs. More precisely, we prove that there exists an absolute constant $δ > 0$ such that for all $c$ sufficiently large, there exist graphs $G$ and $H$ with chromatic number at least $(1 + δ) c$ for which $χ (G \times H) \leq c$ .