图的独立性和匹配杂波的困难性
The hardness of the independence and matching clutter of a graph
摘要：
{ \it杂波}（或{ \it反链}或{ \it Sperner家族}）$L$是一对$(V,E)$，其中$V$是一个有限集，$E$是$V$的子集家族，其中没有一个是另一个的子集。通常，将$V$的元素称为$L$的{ \it顶点}，将$E$的元素称为$L$的{ \it边}。如果$s_e$不是另一边的子集，则杂波的边$e$的子集$s_e$称为$e$的{ \it recognizing}。杂波边缘$e$的{ \it硬度}是$e\textrm{'s}$最小识别子集的大小与$e$大小的比值。杂波的硬度是其边缘的最大硬度。我们研究了图的独立集和匹配所产生的杂波的硬度。
英文摘要：
A {\it clutter} (or {\it antichain} or {\it Sperner family}) $L$ is a pair $(V,E)$, where $V$ is a finite set and $E$ is a family of subsets of $V$ none of which is a subset of another. Usually, the elements of $V$ are called {\it vertices} of $L$, and the elements of $E$ are called {\it edges} of $L$. A subset $s_e$ of an edge $e$ of a clutter is called {\it recognizing} for $e$, if $s_e$ is not a subset of another edge. The {\it hardness} of an edge $e$ of a clutter is the ratio of the size of $e\textrm{'s}$ smallest recognizing subset to the size of $e$. The hardness of a clutter is the maximum hardness of its edges. We study the hardness of clutters arising from independent sets and matchings of graphs.
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。
