AbstractIt is shown that an n-edge connected graph has at least ⌈(n − 1)2⌉ pairwise edge-disjoint spanning trees. This bound is best possible in general. A maximal planar graph with four or more vertices contains two edge-disjoint spanning trees. For a maximal toroidal graph, this number is three
AbstractWe show that for any two natural numbers k,ℓ there exist (smallest natural numbers fℓ(k)(gℓ(...
AbstractFor each n and for each r⩽n−3 we obtain the maximum number of edges of a connected graph wit...
If X is a collection of edges in a graph G, let G/X denote the contraction of X. Following a questio...
AbstractIt is shown that an n-edge connected graph has at least ⌈(n − 1)2⌉ pairwise edge-disjoint sp...
AbstractIn this paper, we present some sharp upper bounds for the number of spanning trees of a conn...
The spanning tree packing number of a connected graph G, denoted by T(G), is the maximum number of e...
AbstractThe path-connectivity of a graph G is the maximal k for which between any k pairs of vertice...
Richard Ehrenborg conjectured that in a bipartite graph G with parts X and Y, the number of spanning...
International audienceThe search of spanning trees with interesting disjunction properties has led t...
The search of spanning trees with interesting disjunction properties has led to the introduction of ...
We prove that every connected graph G of order n has a spanning tree T such that for every edge e of...
AbstractPartially answering a question of Paul Seymour, we obtain a sufficient eigenvalue condition ...
AbstractWe prove that every connected graph G of order n has a spanning tree T such that for every e...
AbstractIn this paper it is proved that for any fixed r and k the number T(G; n, k) of spanning tree...
AbstractWe give a short elementary proof of Tutte and Nash-Williams’ characterization of graphs with...
AbstractWe show that for any two natural numbers k,ℓ there exist (smallest natural numbers fℓ(k)(gℓ(...
AbstractFor each n and for each r⩽n−3 we obtain the maximum number of edges of a connected graph wit...
If X is a collection of edges in a graph G, let G/X denote the contraction of X. Following a questio...
AbstractIt is shown that an n-edge connected graph has at least ⌈(n − 1)2⌉ pairwise edge-disjoint sp...
AbstractIn this paper, we present some sharp upper bounds for the number of spanning trees of a conn...
The spanning tree packing number of a connected graph G, denoted by T(G), is the maximum number of e...
AbstractThe path-connectivity of a graph G is the maximal k for which between any k pairs of vertice...
Richard Ehrenborg conjectured that in a bipartite graph G with parts X and Y, the number of spanning...
International audienceThe search of spanning trees with interesting disjunction properties has led t...
The search of spanning trees with interesting disjunction properties has led to the introduction of ...
We prove that every connected graph G of order n has a spanning tree T such that for every edge e of...
AbstractPartially answering a question of Paul Seymour, we obtain a sufficient eigenvalue condition ...
AbstractWe prove that every connected graph G of order n has a spanning tree T such that for every e...
AbstractIn this paper it is proved that for any fixed r and k the number T(G; n, k) of spanning tree...
AbstractWe give a short elementary proof of Tutte and Nash-Williams’ characterization of graphs with...
AbstractWe show that for any two natural numbers k,ℓ there exist (smallest natural numbers fℓ(k)(gℓ(...
AbstractFor each n and for each r⩽n−3 we obtain the maximum number of edges of a connected graph wit...
If X is a collection of edges in a graph G, let G/X denote the contraction of X. Following a questio...
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