论文标题
树分解和多方面的分离
Tree decompositions and many-sided separations
论文作者
论文摘要
图$ g $的分离是$ v（g）$的分区$（a_1，a_2，c）$，因此$ a_1 $是$ a_2 $的抗议。罗伯逊（Robertson）和西摩（Seymour）的Graph Minors项目的经典结果指出，树木分解与分离的层流集合之间存在对应关系。图$ g $的多面分离是$ v（g）$的分区$（a_1，\ ldots，a_k，c）$，因此$ a_i $对于所有$ 1 \ leq i <j \ j \ j \ leq k $ a_i $ a_i $ a_i $ a_j $。在本说明中，我们显示了具有特定奇偶校验特性的树分解之间的对应关系，称为落叶树分解和多面分离的层流集合。
A separation of a graph $G$ is a partition $(A_1, A_2, C)$ of $V(G)$ such that $A_1$ is anticomplete to $A_2$. A classic result from Robertson and Seymour's Graph Minors Project states that there is a correspondence between tree decompositions and laminar collections of separations. A many-sided separation of a graph $G$ is a partition $(A_1, \ldots, A_k, C)$ of $V(G)$ such that $A_i$ is anticomplete to $A_j$ for all $1 \leq i < j \leq k$. In this note, we show a correspondence between tree decompositions with a certain parity property, called deciduous tree decompositions, and laminar collections of many-sided separations.
