Searching paths of constant bandwidth

Abstract

As a generalization of paths, the notion of paths of bandwidth w is introduced. We show that, for a given constant w >= 1, the corresponding search problem for such a path of length k in a given graph is NP-complete and fixed-parameter tractable in the parameter k, like this is known for the special case w=1, the LONGEST PATH problem. We state the FPT algorithm in terms of a guess and check protocol which uses witnesses of size polynomial in the parameter.