Arc-Disjoint Paths in Expander 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,...

Disjoint Paths in Symmetric Digraphs

Given a number of requests `, we propose a polynomial-time algorithm for finding ` disjoint paths in a symmetric directed graph. It is known that the problem of finding ` ≥ 2 disjoint paths in a directed graph is NP-hard [S. Fortune, J. Hopcroft, J. Wyllie, The directed subgraph homeomorphism problem, Journal of Theoretical Computer Science 10 (2) (1980) 111–121]. However, by studying minimal s...

Two Arc Disjoint Paths in Eulerian Diagraphs

Let G be an Eulerian digraph, and fx 1 ; x 2 g; fy 1 ; y 2 g be two pairs of vertices in G. A directed path from a vertex s to a vertex t is called a st-path. An instance (G; fx 1 ; x 2 g; fy 1 ; y 2 g) is called feasible if there is a choice of h; i; j; k with fh; ig = fj; kg = f1; 2g such that G has two arc-disjoint x h x i and y j y k -paths. In this paper, we characterize the structure of m...