纠缠3的无向图
Undirected Graphs of Entanglement 3
摘要：
纠缠度是有向图的复杂性度量，起源于不动点逻辑。它的组合目的是度量有向图中圈的嵌套深度。我们解决的问题，最多$k$纠缠图的结构特征。到目前为止，只知道部分结果：$k=1$的有向图和$k=2$的无向图。本文研究了$k=3$的无向图的结构。我们的主要工具是所谓的\emph{Tutte's decomposition}的2-连通图成圈和3-连通组件成树状的时尚。我们将给出Tutte树是纠缠3的2-连通图的树分解的必要条件。
英文摘要：
Entanglement is a complexity measure of digraphs that origins in fixed-point logics. Its combinatorial purpose is to measure the nested depth of cycles in digraphs. We address the problem of characterizing the structure of graphs of entanglement at most $k$. Only partial results are known so far: digraphs for $k=1$, and undirected graphs for $k=2$. In this paper we investigate the structure of undirected graphs for $k=3$. Our main tool is the so-called \emph{Tutte's decomposition} of 2-connected graphs into cycles and 3-connected components into a tree-like fashion. We shall give necessary conditions on Tutte's tree to be a tree decomposition of a 2-connected graph of entanglement 3.
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。
