Computing Cutwidth and Pathwidth of Semi-complete Digraphs

Years and Authors of Summarized Original Work

• 2012; Chudnovsky, Fradkin, Seymour

• 2013; Fradkin, Seymour

• 2013; Fomin, Pilipczuk

• 2013; Pilipczuk

• 2013; Fomin, Pilipczuk

Problem Definition

Recall that a simple digraph T is a tournament if for every two vertices u, v ∈ V (T), exactly one of the arcs (u, v) and (v, u) exists in T. If we relax this condition by allowing both these arcs to exist at the same time, then we obtain the definition of a semi-complete digraph. We say that a digraph T contains a digraph H as a topological minor if one can map vertices of H to different vertices of T, and arcs of H to directed paths connecting respective images of the endpoints that are internally vertex disjoint. By relaxing vertex disjointness to arc disjointness, we obtain the definition of an immersion.¹ Finally, we say that T contains H as a minor if vertices of H can be mapped to vertex disjoint strongly connected subgraphs of T in such a manner that for every arc (u, v) of H, there...