A new lower bound on upper irredundance in the queens' graph
type: Item
instance of: scholarly article
title: A new lower bound on upper irredundance in the queens' graph
zbMATH Open document ID: 1008.05112
DOI: 10.1016/S0012-365X(01)00467-8
author: Matthew D. Kearse
author: Peter B. Gibbons
published in: Discrete Mathematics
publication date: 2002-12-02T00:00:00Z
review text: 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.
reviewed by: Bohdan Zelinka
Mathematics Subject Classification ID: 05C69
Mathematics Subject Classification ID: 05C35
zbMATH DE Number: 1838922
zbMATH Keywords: chessboard
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1838922