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## Completely Independent Spanning Trees in Some Regular Graphs

Benoit Darties
Nicolas Gastineau
• Fonction : Auteur
• PersonId : 960240
Olivier Togni

#### Résumé

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 $k$.

#### Domaines

Informatique [cs] Mathématique discrète [cs.DM]

### Dates et versions

hal-01066448 , version 1 (20-09-2014)

### Identifiants

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

### Citer

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

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