Four Edge-Independent Spanning Trees

On Constructing Three Edge Independent Spanning Trees

Abstract. In this paper, we show that a prior result by Khuller and Schieber on the construction of k edge independent spanning trees in a k edge-connected graph fails under certain scenarios. We illustrate the failing of the algorithm with an example and identify the cause, which we refer to as the partial order inversion. For the case of k = 3, we develop a method to compute three edge indepe...

Edge Disjoint Spanning Trees ∗

Let Zm be the cyclic group of order m ≥ 3. A graph G is Zm-connected if G has an orientation D such that for any mapping b : V (G) 7→ Zm with ∑ v∈V (G) b(v) = 0, there exists a mapping f : E(G) 7→ Zm − {0} satisfying ∑ e∈E+ D (v) f(e) − ∑ e∈E− D (v) f(e) = b(v) in Zm for any v ∈ V (G); and a graph G is strongly Zm-connected if, for any mapping θ : V (G) → Zm with ∑ v∈V (G) θ(v) = |E(G)| in Zm, ...

Edge-connectivity and edge-disjoint spanning trees

where the minimum is taken over all subsets X of E(G) such that ω(G − X) − c > 0. In this paper, we establish a relationship 7 between λc(G) and τc−1(G), which gives a characterization of the edge-connectivity of a graph G in terms of the spanning tree 8 packing number of subgraphs of G. The digraph analogue is also obtained. The main results are applied to show that if a graph G is 9 s-hamilto...

A Linear-Time Algorithm to Find Four Independent Spanning Trees in Four-Connected Planar Graphs

Given a graph G, a designated vertex r and a natural number k, we wish to find k “independent” spanning trees of G rooted at r, that is, k spanning trees such that, for any vertex v, the k paths connecting r and v in the k trees are internally disjoint in G. In this paper we give a linear-time algorithm to find four independent spanning trees in a 4-connected planar graph rooted at any vertex.

Edge Operations on Non-Crossing Spanning Trees