Résumé : An elimination tree for a connected graph $G$ is a rooted tree on the vertices of $G$ obtained by choosing a root x and recursing on the connected components of G−x to produce the subtrees of x. Elimination trees appear in many guises in computer science and discrete mathematics, and they encode many interesting combinatorial objects, such as bitstrings, permutations and binary trees. We apply the recent Hartung-Hoang-Mütze-Williams combinatorial generation framework to elimination trees, and prove that all elimination trees for a chordal graph $G$ can be generated by tree rotations using a simple greedy algorithm. This yields a short proof for the existence of Hamilton paths on graph associahedra of chordal graphs. Graph associahedra are a general class of high-dimensional polytopes introduced by Carr, Devadoss, and Postnikov, whose vertices correspond to elimination trees and whose edges correspond to tree rotations. As special cases of our results, we recover several classical Gray codes for bitstrings, permutations and binary trees, and we obtain a new Gray code for partial permutations. This is a joint work with Arturo Merino (TU Berlin) and Torsten Mütze (U. Warwick), to be presented at SODA'22.

 [arXiv]

Dernière modification : Monday 27 May 2024

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