Abstract
The clique-chromatic number χc(G) of graph G is defined as the minimum number k such that there exists a colouring of the vertices of G in k colours that satisfies the following property: all maximal cliques in G (except for the isolated vertices) contain vertices of at least two colours. In this paper we significantly improve lower bounds on this value for some families of Johnson graphs. We also obtain a new upper bound on clique-chromatic number for G(n,r,r−1) and G(n,3,1). Finally, we provide the exact value of clique-chromatic number for G(n,2,1).
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