Abstract
The minimum number of queens which can be placed on ann × n chessboard so that all other squares are dominated by at least one queen but no queen covers another, is shown to be less than 0.705n + 2.305.
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Rouse Ball, W.W.: Mathematical Recreations and Problems of Past and Present Times. London: MacMillan, 1892
Berge, C.: Theory of Graphs, p. 41. London: Methuen, 1962
Berman, P.: Problem 122. P. Mu Epsilon J.3, 412 (1963)
Cockayne, E.J.: Chessboard Domination Problems (submitted)
Cockayne, E.J., Hedetniemi, S.T.: A Note on the diagonal queens domination problem. J. Comb. Theory (A)42, 137–139 (1986)
Gamble, B., Shepherd, B., Cockayne, E.J.: Domination of chessboards by queens on a column. ARS Comb.19, 105–118 (1985)
Guy, R.K.: Unsolved Problems in Number Theory, Vol. 1. New York: Springer-Verlag, 1981
de Jaenisch, C.F.: Applications de l'Analyse Mathématique au Jeu des Échecs. Petrograd 1862
Welch, L. (Private Communication)
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Cockayne, E.J., Spencer, P.H. On the independent queens covering problem. Graphs and Combinatorics 4, 101–110 (1988). https://doi.org/10.1007/BF01864158
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DOI: https://doi.org/10.1007/BF01864158