Abstract We significantly improve lower bounds on the clique-chromatic numbers for some families of Johnson graphs. A new upper bound on the clique-chromatic numbers for G ( n , r , r – 1) and G ( n , 3, 1) is obtained. Finally, the exact value of the clique-chromatic number for G ( n , 2, 1) is provided.

中文翻译：

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Johnson 图的 Clique-Chromatic 数的新边界

摘要 我们显着改善了一些约翰逊图族的团色数的下界。获得了 G ( n , r , r – 1) 和 G ( n , 3, 1) 的团色数的新上限。最后，提供了 G ( n , 2, 1) 的团色数的确切值。