Lower Bounds on Edge Searching

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.