Three-fast-searchable graphs

Abstract

In the edge searching problem searchers move from vertex to vertex in a graph to capture an invisible fast intruder that may occupy either vertices or edges. Fast searching is a monotonic internal model in which at every move a new edge of the graph G must be guaranteed to be free of the intruder. That is once all searchers are placed the graph G is cleared in exactly vertical bar E(G)vertical bar moves. Such a restriction obviously necessitates a larger number of searchers. We examine this model and characterize graphs for which 2 or 3 searchers are sufficient. We prove that the corresponding decision problem is NP-complete. (C) 2013 Elsevier B.V. All rights reserved.