超图的2-截面的树宽
The treewidth of 2-section of hypergraphs
AI总结：
本文研究线性超图的2-截面的树宽，利用超图的最小度、最大度、反秩和平均秩确定其上下界，并提供通过超图参数估计任意图树宽界限的方法。
摘要：
设$H=(V,F)$是一个无环的简单超图。若对于任意$f,g\in F$且$f\not=g$，有$|f\cap g|\le 1$，则称$H$为线性的。$H$的$2$-截面，记为$[H]_2$，是一个图，其顶点集为$V([H]_2)=V$，且对于任意$u,v\in V([H]_2)$，$uv\in E([H]_2)$当且仅当存在$f\in F$使得$u,v\in f$。图的树宽是结构图论和算法图论中的一个重要不变量。本文考虑线性超图的$2$-截面的树宽。我们将利用线性超图的最小度、最大度、反秩和平均秩来确定其$2$-截面树宽的上界和下界。由于对于任意图$G$，存在一个线性超图$H$使得$[H]_2\cong G$，我们提供了一种通过超图的参数来估计图的树宽界限的方法。
英文摘要：
Let $H=(V,F)$ be a simple hypergraph without loops. $H$ is called linear if $|f\cap g|\le 1$ for any $f,g\in F$ with $f\not=g$. The $2$-section of $H$, denoted by $[H]_2$, is a graph with $V([H]_2)=V$ and for any $ u,v\in V([H]_2)$, $uv\in E([H]_2)$ if and only if there is $ f\in F$ such that $u,v\in f$. The treewidth of a graph is an important invariant in structural and algorithmic graph theory. In this paper, we consider the treewidth of the $2$-section of a linear hypergraph. We will use the minimum degree, maximum degree, anti-rank and average rank of a linear hypergraph to determine the upper and lower bounds of the treewidth of its $2$-section. Since for any graph $G$, there is a linear hypergraph $H$ such that $[H]_2\cong G$, we provide a method to estimate the bound of treewidth of graph by the parameters of the hypergraph.
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。
