An improved upper bound for queens domination numbers

We consider the domination number of the queens graph Qn and show that if, for some -xed k, there is a dominating set of Q4k+1 of a certain type with cardinality 2k + 1, then for any n large enough, (Qn)6 [(3k + 5)=(6k + 3)]n + O(1). The same construction shows that for any m¿ 1 and n = 2(6m − 1)(2k + 1) − 1, (Q n)6 [(2k + 3)=(4k + 2)]n + O(1), where Q n is the toroidal n× n queens graph. c © 2003 Elsevier Science B.V. All rights reserved.