A new lower bound on upper irredundance in the queens' graph (Q1849927)

The queens' graph \(Q_n\) is the graph whose vertex set is the set of all squares of the \(n\times n\) chessboard and in which two vertices are adjacent if and only if they can be reached from one another by one move of the chess queen. An irredundant set of queens on it has the property that each queen attacks at least one square which is attacked by no other queen. The number of elements of an irredundant set of queens is the upper irredundance \(\text{IR}(Q_n)\) of \(Q_n\). In the paper the inequality \(\text{IR}(Q_k)\geq 6k^3- 29k^2- O(k)\) for even \(k\geq 6\) is stated.