Arc-disjoint strong spanning subdigraphs in compositions and products of digraphs

Spanning k-arc-strong subdigraphs with few arcs in k-arc-strong tournaments

Given a k-arc-strong tournament T , we estimate the minimum number of arcs possible in a k-arc-strong spanning subdigraph of T . We give a construction which shows that for each k ≥ 2 there are tournaments T on n vertices such that every k-arc-strong spanning subdigraph of T contains at least nk+ k(k−1) 2 arcs. In fact, the tournaments in our construction have the property that every spanning s...

Arc-disjoint spanning sub(di)graphs in digraphs

4 We prove that a number of natural problems concerning the existence of arc-disjoint directed 5 and “undirected” (spanning) subdigraphs in a digraph are NP-complete. Among these are the 6 following of which the first settles an open problem due to Thomassé (see e.g. [1, Problem 9.9.7] 7 and [3, 5]) and the second settles an open problem posed in [3]. 8 • Given a directed graph D and a vertex s...

Arc-Disjoint Paths in Expander Digraphs

Arc-Disjoint Paths in Decomposable Digraphs

4 We prove that the weak k-linkage problem is polynomial for every fixed k for totally Φ5 decomposable digraphs, under appropriate hypothesis on Φ. We then apply this and recent results 6 by Fradkin and Seymour (on the weak k-linkage problem for digraphs of bounded independence 7 number or bounded cut-width) to get polynomial algorithms for some class of digraphs like quasi8 transitive digraphs...

Arc-Disjoint Paths and Trees in 2-Regular Digraphs

An out-(in-)branching B s (B − s ) rooted at s in a digraph D is a connected spanning subdigraph of D in which every vertex x 6= s has precisely one arc entering (leaving) it and s has no arcs entering (leaving) it. We settle the complexity of the following two problems: • Given a 2-regular digraph D, decide if it contains two arc-disjoint branchings B u , B − v . • Given a 2-regular digraph D,...