Arc-disjoint circuits in digraphs

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,...

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...

Complexity of trails, paths and circuits in arc-colored digraphs

We deal with different algorithmic questions regarding properly arc-colored s-t trails, paths and circuits in arc-colored digraphs. Given an arc-colored digraph D with c ≥ 2 colors, we show that the problem of determining the maximum number of arc disjoint properly arc-colored s-t trails can be solved in polynomial time. Surprisingly, we prove that the determination of a properly arc-colored s-...