Hedetniemi's conjecture for uncountable graphs

TL;DR

This paper proves that within Godel's constructible universe, for any infinite successor cardinal, there exist large graphs with high chromatic number whose tensor product is only countably chromatic, challenging assumptions about graph coloring.

Contribution

It demonstrates the existence of specific uncountable graphs with high chromatic number whose tensor product has low chromatic number in Godel's constructible universe.

Findings

Existence of graphs with size and chromatic number k

Tensor product of these graphs is countably chromatic

Results hold in Godel's constructible universe

Abstract

It is proved that in Godel's constructible universe, for every infinite successor cardinal k, there exist graphs G and H of size and chromatic number k, for which the tensor product graph (G x H) is countably chromatic.