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1. We first show a lower bound of 2N/3-1 for the connected minimum queendomination (or cover) problem on the NXN chessboard - the upper bound is only 2higher at most and is easy to show. 2. We then define the k-colored connectedminimum 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 lowerbounds LB(N, k) until one reaches the simple domination lower bound of floorN/2. 3. We also discuss extensions of the connected domination problem andadditional directions.

Tight lower bounds for connected queen domination problems on the chessboard