Graph associahedra are generalized permutohedra arising as special cases of nestohedra and hypergraphic polytopes. The graph associahedron of a graph $G$ encodes the combinatorics of search trees on $G$, defined recursively by a root $r$ together with search trees on each of the connected components of $G-r$. In particular, the skeleton of the graph associahedron is the rotation graph of those search trees. We investigate the diameter of graph associahedra as a function of some graph parameters. It is known that the diameter of the associahedra of paths of length $n$, the classical associahedra, is $2n-6$ for a large enough $n$. We give a tight bound of $\Theta(m)$ on the diameter of trivially perfect graph associahedra on $m$ edges. We consider the maximum diameter of associahedra of graphs on $n$ vertices and of given tree-depth, treewidth, or pathwidth, and give lower and upper bounds as a function of these parameters. Finally, we prove that the maximum diameter of associahedra of graphs of pathwidth two is $\Theta (n\log n)$.
翻译：osociaedra 的图形是通用的 motoohedra, 它们是作为 eongohedra 和 ypegraphic potitops 的特殊例子产生的 。 一个图形 $G$ 的图形 将搜索树的组合编码为$G$, 由根 $- r$ 和每个连接的 $G- r$ 组件的搜索树组成。 特别是, 图形 associaedra 的骨架是这些搜索树的旋转图。 我们把图形 associahedra 的直径作为某些图形参数的函数。 已知长于 $$( G$) 的路径, 古典 as sociahedra 的直径直径为$2n-6 美元, 其直径为$- m) 的直径, 其直径为$- 直径, 直径为 直径和 直径的双直径。
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