Hadwiger's conjecture for hypergraphs

Dominic van der Zypen

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arXiv · 2607.27243

Hadwiger's conjecture for hypergraphs

Dominic van der Zypen

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Abstract

In 1943, Hadwiger formulated his celebrated conjecture, connecting the chromatic number $\chi(G)$ of a finite, simple, undirected graph with the cardinality of the largest complete minor, $\eta(G)$. The disjoint union of all finite complete graphs shows that Hadwiger's conjecture fails for infinite, but a slightly weaker version is true in these graphs, and open for finite graphs. In this note we generalize that weaker version to hypergraphs and provide a simple, general, and purely set-theoretical formulation of Hadwiger's conjecture.

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BibTeX RIS

Dominic van der Zypen. 2026-07-27. Hadwiger's conjecture for hypergraphs. https://arxiv.org/abs/2607.27243

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