Add to ORKGThe search of spanning trees with interesting disjunction properties has led to the introduction of edge-disjoint spanning trees, independent spanning trees and more recently completely independent spanning trees. We group together these notions by defining (i, j)-disjoint spanning trees, where i (j, respectively) is the number of vertices (edges, respectively) that are shared by more than one tree. We illustrate how (i, j)-disjoint spanning trees provide some nuances between the existence of disjoint connected dominating sets and completely independent spanning trees. We prove that determining if there exist two (i, j)-disjoint spanning trees in a graph G is NP-complete, for every two positive integers i and j. Moreover we prove that for s...
AbstractFarber et al. (1985) proved that any pair of edge-disjoint spanning trees in a graph can be ...
Let $k\ge 2$ be an integer and $T_1,\ldots, T_k$ be spanning trees of a graph $G$. If for any pair o...
Let $k\ge 2$ be an integer and $T_1,\ldots, T_k$ be spanning trees of a graph $G$. If for any pair o...
International audienceThe search of spanning trees with interesting disjunction properties has led t...
International audienceThe search of spanning trees with interesting disjunction properties has led t...
International audienceIn this extended abstract, we only consider connected graphs. Let k ≥ 2 be an ...
International audienceIn this extended abstract, we only consider connected graphs. Let k ≥ 2 be an ...
AbstractIt is shown that an n-edge connected graph has at least ⌈(n − 1)2⌉ pairwise edge-disjoint sp...
Two spanning trees T1 and T2 of a graph G are completely independent if, for any two vertices u and ...
Let T1, T2, . . . , Tk be spanning trees of a graph G. For any two vertices u, v of G, if the paths ...
The spanning tree packing number of a connected graph G, denoted by T(G), is the maximum number of e...
International audienceLet k >= 2 be an integer and T-1,..., T-k be spanning trees of a graph G. If f...
International audienceLet k >= 2 be an integer and T-1,..., T-k be spanning trees of a graph G. If f...
AbstractIn this note, we define completely independent spanning trees. We say that T1,T2,…,Tk are co...
International audienceLet k >= 2 be an integer and T-1,..., T-k be spanning trees of a graph G. If f...
AbstractFarber et al. (1985) proved that any pair of edge-disjoint spanning trees in a graph can be ...
Let $k\ge 2$ be an integer and $T_1,\ldots, T_k$ be spanning trees of a graph $G$. If for any pair o...
Let $k\ge 2$ be an integer and $T_1,\ldots, T_k$ be spanning trees of a graph $G$. If for any pair o...
International audienceThe search of spanning trees with interesting disjunction properties has led t...
International audienceThe search of spanning trees with interesting disjunction properties has led t...
International audienceIn this extended abstract, we only consider connected graphs. Let k ≥ 2 be an ...
International audienceIn this extended abstract, we only consider connected graphs. Let k ≥ 2 be an ...
AbstractIt is shown that an n-edge connected graph has at least ⌈(n − 1)2⌉ pairwise edge-disjoint sp...
Two spanning trees T1 and T2 of a graph G are completely independent if, for any two vertices u and ...
Let T1, T2, . . . , Tk be spanning trees of a graph G. For any two vertices u, v of G, if the paths ...
The spanning tree packing number of a connected graph G, denoted by T(G), is the maximum number of e...
International audienceLet k >= 2 be an integer and T-1,..., T-k be spanning trees of a graph G. If f...
International audienceLet k >= 2 be an integer and T-1,..., T-k be spanning trees of a graph G. If f...
AbstractIn this note, we define completely independent spanning trees. We say that T1,T2,…,Tk are co...
International audienceLet k >= 2 be an integer and T-1,..., T-k be spanning trees of a graph G. If f...
AbstractFarber et al. (1985) proved that any pair of edge-disjoint spanning trees in a graph can be ...
Let $k\ge 2$ be an integer and $T_1,\ldots, T_k$ be spanning trees of a graph $G$. If for any pair o...
Let $k\ge 2$ be an integer and $T_1,\ldots, T_k$ be spanning trees of a graph $G$. If for any pair o...