On \(b\)-coloring of the Kneser graphs
Let \(G\) be a graph without loops and multiple edges. A \(b\)-colouring of \(G\) by \(k\) colours is a proper \(k\)-colouring of \(G\) such that in each colour class there is a vertex having neighbours in all the other \(k-1\) colour classes. The \(b\)-chromatic number of a graph \(G\) is the maximum number \(k\) for which \(G\) has a \(b\)-colouring by \(k\) colours. A graph \(G\) is \(b\)-continuous if for every \(k\) between the chroamtic nuumber and the \(b\)-chromatic number there is a \(b\)-colouring of \(G\) by \(k\) colours. In the present paper, \(b\)-colourings of Kneser graphs \(K(n, k)\) are studied. Moreover, it is proved that \(K(n, 2)\) is \(b\)-continuous for \(n\geq 17\).
scientific article; zbMATH DE number 5644957