论文标题
具有界数的超图的分数盖
Fractional Covers of Hypergraphs with Bounded Multi-Intersection
论文作者
论文摘要
分数（超）图理论涉及当考虑其他整数值（超级）图形不变的分数类似物时，出现的特定问题。本文的重点是超图的分数边缘盖。我们的主要技术结果概括并统一了以前的条件，在这些条件下，分数边缘盖的支撑大小与超图本身的大小无关。这使我们可以扩展以前的障碍结果，以检查给定超图的分数高宽度是否为某些常数$ k $的$ \ leq k $。我们还展示了我们的结果如何转化为分数顶点盖。
Fractional (hyper-)graph theory is concerned with the specific problems that arise when fractional analogues of otherwise integer-valued (hyper-)graph invariants are considered. The focus of this paper is on fractional edge covers of hypergraphs. Our main technical result generalizes and unifies previous conditions under which the size of the support of fractional edge covers is bounded independently of the size of the hypergraph itself. This allows us to extend previous tractability results for checking if the fractional hypertree width of a given hypergraph is $\leq k$ for some constant $k$. We also show how our results translate to fractional vertex covers.
