Geodesic
Counterexamples to Hedetniemi's conjecture and infinite Boolean lattices
Commentationes Mathematicae Universitatis Carolinae, Tome 63 (2022) no. 3, pp. 315-327.

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We prove that for any $c \geq 5$, there exists an infinite family $(G_n )_{n\in \mathbb{N}}$ of graphs such that $\chi(G_n) > c$ for all $n\in \mathbb{N}$ and $\chi(G_m \times G_n) \leq c$ for all $m \neq n$. These counterexamples to Hedetniemi's conjecture show that the Boolean lattice of exponential graphs with $K_c$ as a base is infinite for $c \geq 5$.
DOI : 10.14712/1213-7243.2023.003
Classification : 05C15
Keywords: categorical product; graph colouring; Hedetniemi's conjecture 
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Tardif, Claude. Counterexamples to Hedetniemi's conjecture and infinite Boolean lattices. Commentationes Mathematicae Universitatis Carolinae, Tome 63 (2022) no. 3, pp. 315-327. doi : 10.14712/1213-7243.2023.003. http://geodesic.mathdoc.fr/articles/10.14712/1213-7243.2023.003/

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