Cutwidth I: A linear time fixed parameter algorithm

Abstract

The cutwidth of a graph G is the smallest integer k such that the vertices of G can be arranged in a linear layout [ v 1 , … , v n ] in such a way that, for every i = 1 , … , n − 1 , there are at most k edges with one endpoint in { v 1 , … , v i } and the other in { v i + 1 , … , v n } . In this paper we provide, for any constant k, a linear time algorithm that for any input graph G, answers whether G has cutwidth at most k and, in the case of a positive answer, outputs the corresponding linear layout.