Abstract
The chromatic numbers of queen\(\,-\,\) \({{n}^2}\) graphs are difficult to determine when n > 9 and n is a multiple of 2 or 3. In previous works [6, 7], we have proven that this number (denoted \(\chi _{n}\,\)) is equal to n for \(n \in \{12,14,15,16,18,20,21,22,24,28,32\}\) and that \(\chi _{10}\,\)\(=11\). This article describes how, by extending slightly further the previous work, the chromatic number of queen\(\,-\,\) \({{26}^2}\) and queen\(\,-\,\) \({{30}^2}\) can be obtained. A more general result, proving that \(\chi _{2n}\,\)\(=2n\) and \(\chi _{3n}\,\)\(=3n\) for infinitely many values of n, is then presented.
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Vasquez, M., Vimont, Y. (2018). On Solving the Queen Graph Coloring Problem. In: Brankovic, L., Ryan, J., Smyth, W. (eds) Combinatorial Algorithms. IWOCA 2017. Lecture Notes in Computer Science(), vol 10765. Springer, Cham. https://doi.org/10.1007/978-3-319-78825-8_20
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