Disjoint Paths in Symmetric Digraphs

Disjoint paths in arborescences

An arborescence in a digraph is a tree directed away from its root. A classical theorem of Edmonds characterizes which digraphs have λ arc-disjoint arborescences rooted at r. A similar theorem of Menger guarantees λ strongly arc disjoint rv-paths for every vertex v, where “strongly” means no two paths contain a pair of symmetric arcs. We prove that if a directed graph D contains two arc-disjoin...

Comments on "Line Digraph Iterations and Connectivity Analysis of de Bruijn and Kautz Graphs"

The aim of this note is to present some counterexamples to the results in the paper by Du, Lyuu and Hsu published in this Transactions 1]. We present in this paper, for any d 2, a digraph G 2 L (d; 4) \ L (d ? 1; 4) such that LG 6 2 L (d ? 1; 5) and L 2 G 6 2 L (d; 6). Therefore, this is a counterexample to Lemma 3.2 and Theorem 3.3 of 1]. The digraphs we consider here are members of a family o...

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...

Constant Congestion Routing of Symmetric Demands in Planar Directed Graphs

We study the problem of routing symmetric demand pairs in planar digraphs. The input consists of a directed planar graph G = (V, E) and a collection of k source-destination pairs M = {s1t1, . . . , sktk}. The goal is to maximize the number of pairs that are routed along disjoint paths. A pair siti is routed in the symmetric setting if there is a directed path connecting si to ti and a directed ...

Arc-Disjoint Paths in Expander Digraphs