An improved upper bound for queens domination numbers

Authors:
A. P. Burger;C. M. Mynhardt
Affiliations:
Department of Mathematics and Statistics, University of Victoria, P.O. Box 3045, Victoria, BC Canada V8W 3P4;Department of Mathematics and Statistics, University of Victoria, P.O. Box 3045, Victoria, BC Canada V8W 3P4
Venue:
Discrete Mathematics - Special issue: The 18th British combinatorial conference
Year:
2003

Citing 4
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Abstract

We consider the domination number of the queens graph Qn and show that if, for some fixed k, there is a dominating set of Q4k+1 of a certain type with cardinality 2k + 1, then for any n large enough, γ(Qn) ≤ [(3k + 5)/(6k + 3)]n + O(1). The same construction shows that for any m ≥ 1 and n = 2(6m - 1)(2k + 1) - 1, γ(Qnt) ≤ [(2k + 3)/(4k + 2)]n + O(1), where Qnt is the toroidal n × n queens graph.