Generating Solutions to the n-Queens Problem

This work presents procedures for generating solutions to the n-Queens problem using 2-circulant matrices, maximal cliques of graphs and 0-1 integer programming. Some constructions on matrices to prove that a solution exists for n > 3 are also presented. The use of maximal cliques is an application from the field of graph theory; the use of 0-1 integer programming is an application from the field of operations research.