Fast searching games on graphs

Authors:
Donald Stanley;Boting Yang
Affiliations:
Department of Mathematics and Statistics, University of Regina, Regina, Canada;Department of Computer Science, University of Regina, Regina, Canada
Venue:
Journal of Combinatorial Optimization
Year:
2011

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Abstract

Given a graph, suppose that intruders hide on vertices or along edges of the graph. The fast searching problem is to find the minimum number of searchers required to capture all the intruders satisfying the constraint that every edge is traversed exactly once and searchers are not allowed to jump. In this paper, we prove lower bounds on the fast search number. We present a linear time algorithm to compute the fast search number of Halin graphs and their extensions. We present a quadratic time algorithm to compute the fast search number of cubic graphs.