Ambush Cops and Robbers

A variation of the Cops and Robber game is introduced in which the robber side consists of two robbers. The cops win by moving onto the same vertex as one of the robbers after a finite number of moves. As in the original game, the robber side can win by avoiding capture indefinitely. In this version, however, the robbers can also win by both moving onto the same vertex as the cop at the same time. Otherwise, the robbers must be located on distinct vertices. We present structural properties of ambush-copwin graphs, those graphs on which a single cop can guarantee a win. As well, we characterize ambush-copwin graphs of girth $$g \ge 4$$ and classes of ambush-copwin graphs of girth 3, particularly a class of chordal graphs.