The mixed search game against an agile and visible fugitive is monotone

We consider the mixed search game against an agile and visible fugitive. This is variant of classic fugitive on graphs where searchers may be placed to (or removed from) vertices or slide along edges. Moreover, resides edges graph can move at any time unguarded paths. The number a G, denoted avms(G), minimum required capture in this searching variant. Our main result that monotone sense for successful strategy does not increase if we restrict strategies those do permit visit already “clean” edge. means polynomially certified, therefore problem deciding, given G integer k, whether avms(G)≤k NP. proof based introduction notion tight bramble, serves as obstruction corresponding parameter. results imply avms(G) equal Cartesian tree product is, k which minor clique vertices.