Hadwiger's conjecture for hypergraphs

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.

3 pages