A Gray code for arborescences of tournaments
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866910085746262016 |
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| author | Bonamy, Marthe Hoffmann, Michael Legrand-Duchesne, Clément Rote, Günter |
| author_facet | Bonamy, Marthe Hoffmann, Michael Legrand-Duchesne, Clément Rote, Günter |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_28614 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A Gray code for arborescences of tournaments Bonamy, Marthe Hoffmann, Michael Legrand-Duchesne, Clément Rote, Günter Combinatorics Discrete Mathematics 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. |
| title | A Gray code for arborescences of tournaments |
| topic | Combinatorics Discrete Mathematics |
| url | https://arxiv.org/abs/2603.28614 |