2026/07/27 by Dominic van der Zypen
Mathematics · #math.LO #math.CO #msc:03E05 #msc:05C65
2 pages
arxiv created 2026/07/27 · arxiv updated 2026/07/31
In 1943, Hadwiger formulated his celebrated conjecture, connecting the chromatic number χ(G) of a finite, simple, undirected graph with the cardinality of the largest complete minor, η(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, but open for finite graphs. In this note we generalize that weaker version to hypergraphs and providea simple, general, and purely set-theoretical formulation of Hadwiger's conjecture.