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arXiv · 1608.02531

Tight lower bounds for connected queen domination problems on the chessboard

Sneha S. Venkatesan·S. M. Venkatesan
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Abstract

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.

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Sneha S. Venkatesan, S. M. Venkatesan. 2016-08-08. Tight lower bounds for connected queen domination problems on the chessboard. https://arxiv.org/abs/1608.02531

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