A constructive linear time algorithm for small cutwidth*y

The cutwidth of a graph G is deened to be the smallest integer k such that the vertices of G can be arranged in a linear layout v 1 ; : : : ; vn] in such a way that for every i = 1; : : : ; n?1, there are at most k edges with the one endpoint in fv 1 ; : : : ; v i g and the other in fv i+1 ; : : : ; vng. In this paper we show how to construct, 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.