论文标题
等效关系中的完整彩虹匹配
Full rainbow matchings in equivalence relations
论文作者
论文摘要
我们表明，如果多数$ g $具有最大边缘多性性的最多$ \ frac {\ sqrt {n}} {\ log^2 n} $，则由$ n $颜色边缘颜色，以使每个颜色类别都是与cliques的差异，每个颜色都不是2n + o（n）$（n）$（N）$（N）$（n）$（n），然后是一个完整的Vertice，它是一个完整的搭配，它是一个匹配的，它是一个匹配的， 一次。这个渐近地解决了克莱门斯，埃伦穆勒和博克罗夫斯基的一个问题，并且与格林布拉特在[Grinblat 2002]中研究的代数方面的问题有关。
We show that if a multigraph $G$ with maximum edge-multiplicity of at most $\frac{\sqrt{n}}{\log^2 n}$, is edge-coloured by $n$ colours such that each colour class is a disjoint union of cliques with at least $2n + o(n)$ vertices, then it has a full rainbow matching, that is, a matching where each colour appears exactly once. This asymptotically solves a question raised by Clemens, Ehrenmüller and Pokrovskiy, and is related to problems on algebras of sets studied by Grinblat in [Grinblat 2002].
