(Arc-)disjoint flows in networks

(Arc-)disjoint flows in networks

4 We consider the problem of deciding whether a given network with integer capacities has two 5 feasible flows x and y with prescribed balance vectors such that the arcs that carry flow in x are 6 arc-disjoint from the arcs that carry flow in y. This generalizes a number of well-studied problems 7 such as the existence of arc-disjoint out-branchings B s , B + t where the roots s, t may be the s...

Arc-Disjoint Cycles and Feedback Arc Sets

Isaak posed the following problem. Suppose T is a tournament having a minimum feedback arc set which induces an acyclic digraph with a hamiltonian path. Is it true that the maximum number of arc-disjoint cycles in T equals the cardinality of minimum feedback arc set of T? We prove that the answer to the problem is in the negative. Further, we study the number of arc-disjoint cycles through a ve...

Arc-Disjoint Paths in Expander Digraphs

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...

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...