In the game of cops and robbers on a graph G = (V,E), k cops try to catch a robber. On the cop turn, each cop may move to a neighboring vertex or remain in place. On the robberâ€™s turn, he movesâ€¦ (More)

We consider the minimum order graphs with a given cop number k, and we focus especially on the cases k = 2, 3. We prove that the minimum order of a connected graph with cop number 3 is 10, and showâ€¦ (More)

Although a combinatorial interpretation of Macdonald polynomials involving fillings of Ferrers diagrams of partitions has been known since 2004, a general combinatorial proof of a well-known symmetryâ€¦ (More)

In the game of cops and robbers on a graph G = (V,E), k cops try to catch a robber. On the cop turn, each cop may move to a neighboring vertex or remain in place. On the robberâ€™s turn, he movesâ€¦ (More)

In the game of cops and robbers on a graph G = (V,E), k cops try to catch a robber. On the cop turn, each cop may move to a neighboring vertex or remain in place. On the robberâ€™s turn, he movesâ€¦ (More)