Cutwidth I: A linear time fixed parameter algorithm

The cutwidth of a graph G is the smallest integer k such that the vertices of G can be arranged in a linear layout [v1,…,vn] in such a way that, for every i=1,…,n−1, there are at most k edges with one endpoint in {v1,…,vi} and the other in {vi+1,…,vn}. 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.