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.

翻译：分数（超）图理论研究的是在考虑原本整数值的（超）图不变量的分数类比时出现的特定问题。本文聚焦于超图的分数边覆盖。我们的主要技术结果推广并统一了先前关于分数边覆盖支撑集大小独立于超图本身大小有界的条件。这使我们能够扩展先前关于检查给定超图的分数超树宽度是否$\leq k$（其中$k$为常数）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。