Disjoint paths in symmetric digraphs

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...

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...

Edge-disjoint paths in digraphs with bounded independence number

A digraph H is infused in a digraph G if the vertices of H are mapped to vertices of G (not necessarily distinct), and the edges of H are mapped to edge-disjoint directed paths of G joining the corresponding pairs of vertices of G. The algorithmic problem of determining whether a fixed graph H can be infused in an input graph G is polynomial-time solvable for all graphs H (using paths instead o...

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,...