论文标题
在3-均匀的超图中完美匹配的顶点度阈值的度序列加强
A degree sequence strengthening of the vertex degree threshold for a perfect matching in 3-uniform hypergraphs
论文作者
论文摘要
对超图中强力匹配和瓷砖的渐近最低度阈值的研究是组合学研究的生动领域。该领域的一个关键突破是Hàn，Person和Schacht的结果，他们证明了在$ n $ -n $ -vertex $ 3 $ -Graph as $ \ weft（\ frac {5} {5} {9} {9} {9}+o（o（o（of））中，渐近的最低顶点度阈值是完美匹配的。在本文中，我们对此结果进行了改进，给出了一个学位序列结果，所有这些都暗示了Hàn，Person和Schacht的结果，此外，三分之一的顶点具有$ \ frac {1} {1} {9} {9} \ binom {n} {n} {2} {2} {2} $下面的thereshold。此外，我们表明，从某种意义上说，这个结果是紧密的。
The study of asymptotic minimum degree thresholds that force matchings and tilings in hypergraphs is a lively area of research in combinatorics. A key breakthrough in this area was a result of Hàn, Person and Schacht who proved that the asymptotic minimum vertex degree threshold for a perfect matching in an $n$-vertex $3$-graph is $\left(\frac{5}{9}+o(1)\right)\binom{n}{2}$. In this paper we improve on this result, giving a family of degree sequence results, all of which imply the result of Hàn, Person and Schacht, and additionally allow one third of the vertices to have degree $\frac{1}{9}\binom{n}{2}$ below this threshold. Furthermore, we show that this result is, in some sense, tight.
