具有有界多重交的超图的分数覆盖
Fractional Covers of Hypergraphs with Bounded Multi-Intersection
AI总结：
本文研究超图的分数边覆盖，推广并统一了支撑集大小有界性的条件，从而扩展了分数超树宽检查的可处理性结果，并推广到分数顶点覆盖。
摘要：
分数（超）图论研究的是当考虑原本为整数值的（超）图不变量的分数类比时所产生的特定问题。本文的重点是超图的分数边覆盖。我们的主要技术结果推广并统一了先前关于分数边覆盖的支撑集大小可独立于超图自身大小而有界成立的条件。这使我们能够扩展先前关于检查给定超图的分数超树宽是否对某个常数 $k$ 满足 $\leq k$ 的可处理性结果。我们还展示了我们的结果如何转化为分数顶点覆盖。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
