#### Title

On The Queen Domination Problem

#### Document Type

Article

#### Publication Date

12-14-1990

#### Published In

Discrete Mathematics

#### Abstract

A configuration of queens on an m x m chessboard is said to dominate the board if every square either contains a queen or is attacked by a queen. The configuration is said to be non-attacking if no queen attacks another queen. Let f(m) and g(m) equal the minimum number of queens and the minimum number of non-attacking queens, respectively, needed to dominate an m x m chessboard. We prove that: (1) f(m) less-than-or-equal-to 14/23m + O(1), and (2) g(m) less-than-or-equal-to 2/3m + O(1).These are the best upper bounds known at the present time for these functions.

#### Recommended Citation

Charles M. Grinstead; Bruce M. Hahne , '90; and David W. Van Stone , '88.
(1990).
"On The Queen Domination Problem".
*Discrete Mathematics*.
Volume 86,
Issue 1-3.
21-26.

http://works.swarthmore.edu/fac-math-stat/60