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arXiv · 2603.28614

A Gray code for arborescences of tournaments

Marthe Bonamy·Michael Hoffmann·Clément Legrand-Duchesne·Günter Rote
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Abstract

We consider the following question of Knuth: given a directed graph $G$ and a root $r$, can the arborescences of $G$ rooted in $r$ be listed such that any two consecutive arborescences differ by only one arc? Such an ordering is called a pivot Gray code and can be formulated as a Hamiltonian path in the reconfiguration graph of the arborescences of $G$ under arc flips, also called flip graph of $G$. We give a positive answer for tournaments and explore several conditions showing that the flip graph of a directed graph may contain no Hamiltonian cycles.

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Marthe Bonamy, Michael Hoffmann, Clément Legrand-Duchesne, Günter Rote. 2026-03-30. A Gray code for arborescences of tournaments. https://arxiv.org/abs/2603.28614

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