# Completely Independent Spanning Trees in Some Regular Graphs

2 Equipe Combinatoire
Le2i - Laboratoire Electronique, Informatique et Image
Abstract : Let $k\ge 2$ be an integer and $T_1,\ldots, T_k$ be spanning trees of a graph $G$. If for any pair of vertices $(u,v)$ of $V(G)$, the paths from $u$ to $v$ in each $T_i$, $1\le i\le k$, do not contain common edges and common vertices, except the vertices $u$ and $v$, then $T_1,\ldots, T_k$ are completely independent spanning trees in $G$. For $2k$-regular graphs which are $2k$-connected, such as the Cartesian product of a complete graph of order $2k-1$ and a cycle and some Cartesian products of three cycles (for $k=3$), the maximum number of completely independent spanning trees contained in these graphs is determined and it turns out that this maximum is not always $k$.
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Type de document :
Pré-publication, Document de travail
2014
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https://hal-univ-bourgogne.archives-ouvertes.fr/hal-01066448
Contributeur : Nicolas Gastineau <>
Soumis le : samedi 20 septembre 2014 - 13:38:56
Dernière modification le : lundi 13 octobre 2014 - 15:43:25
Document(s) archivé(s) le : dimanche 21 décembre 2014 - 10:16:19

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• HAL Id : hal-01066448, version 1
• ARXIV : 1409.6002

### Citation

Benoit Darties, Nicolas Gastineau, Olivier Togni. Completely Independent Spanning Trees in Some Regular Graphs. 2014. <hal-01066448>

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