Lower bounds on edge searching

Authors:
Brian Alspach;Danny Dyer;Denis Hanson;Boting Yang
Affiliations:
Department of Mathematics and Statistics, University of Regina;Department of Mathematics and Statistics, Memorial University of Newfoundland;Department of Mathematics and Statistics, University of Regina;Department of Computer Science, University of Regina
Venue:
ESCAPE'07 Proceedings of the First international conference on Combinatorics, Algorithms, Probabilistic and Experimental Methodologies
Year:
2007

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Abstract

Searching a network for intruders is an interesting and difficult problem. Edge-searching is one such search model, in which intruders may exist anywhere along an edge. Since finding the minimum number of searchers necessary to search a graph is NP-complete, it is natural to look for bounds on the search number. We show lower bounds on the search number using minimum degree, girth, chromatic number, and colouring number.