论文标题
图联合的树宽和路径
The treewidth and pathwidth of graph unions
论文作者
论文摘要
给定两个$ n $ vertex图$ g_1 $和$ g_2 $的有界树宽，是否有一个$ n $ vertex图$ g $的有界树宽的$ g $，具有子图等质形式为$ g_1 $和$ g_2 $？我们的主要结果是对这个问题的负面答案，从很强的意义上讲：我们证明答案是不是，即使$ g_1 $是二进制树，而$ g_2 $是三元树。我们还提供了有关这种“胶合”的案例的广泛研究。特别是，我们证明，如果$ g_1 $具有treewidth $ k $，而$ g_2 $具有PATHWIDTH $ \ ell $，那么最多有$ k + 3 \ ell + 1 $包含$ g_1 $和$ g_2 $的$ n $ vertex of treewidth of treewidth。
Given two $n$-vertex graphs $G_1$ and $G_2$ of bounded treewidth, is there an $n$-vertex graph $G$ of bounded treewidth having subgraphs isomorphic to $G_1$ and $G_2$? Our main result is a negative answer to this question, in a strong sense: we show that the answer is no even if $G_1$ is a binary tree and $G_2$ is a ternary tree. We also provide an extensive study of cases where such `gluing' is possible. In particular, we prove that if $G_1$ has treewidth $k$ and $G_2$ has pathwidth $\ell$, then there is an $n$-vertex graph of treewidth at most $k + 3 \ell + 1$ containing both $G_1$ and $G_2$ as subgraphs.
