Sweeping graphs with large clique number

Searching a network for intruders is an interesting and often difficult problem. Sweeping (or edge searching) is one such search model, in which intruders may exist anywhere along an edge. It was conjectured that graphs exist for which the connected sweep number is strictly less than the monotonic connected sweep number. We prove that this is true, and the difference can be arbitrarily large. We also show that the clique number is a lower bound on the sweep number.