AI 中文总结
本文将针对无限图成立的稍弱版哈德维格猜想推广到超图，给出其纯集合论表述，该猜想对有限图仍未解决。
AI 中文摘要
1943年，哈德维格提出了著名的哈德维格猜想，将有限简单无向图的色数χ(G)与最大完全子式的基数η(G)联系起来。所有有限完全图的不交并表明，哈德维格猜想对无限图不成立，但对无限图存在稍弱的版本成立，而对有限图该猜想仍未解决。本文将该稍弱版本推广到超图，并给出了哈德维格猜想的一个简单、通用且纯集合论的表述。
英文摘要
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, 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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