标题： 棋盘上连通皇后支配问题的紧下界 显示英文标题

标题： Tight lower bounds for connected queen domination problems on the chessboard

摘要： 1. 我们首先证明在NXN棋盘上的连通最小皇后支配（或覆盖）问题的下界为2N/3-1，而上界最多只高2，并且很容易证明。 2. 然后我们定义k色连通最小皇后支配，并扩展上述证明以证明下界为(2 N - k - 2)/3，其中参数k可以增加以得到递减的下界LB(N, k)，直到达到简单的支配下界floor N/2。 3. 我们还讨论了连通支配问题的扩展和其他方向。 显示英文摘要

摘要： 1. We first show a lower bound of 2N/3-1 for the connected minimum queen domination (or cover) problem on the NXN chessboard - the upper bound is only 2 higher at most and is easy to show. 2. We then define the k-colored connected minimum queen domination, and extend the above proof to show a lower bound of (2 N - k - 2)/3, where the parameter k can be increased to get decreasing lower bounds LB(N, k) until one reaches the simple domination lower bound of floor N/2. 3. We also discuss extensions of the connected domination problem and additional directions.