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In this paper we characterize -chromatic graphs without isolated vertices and connected -chromatic graphs having a minimal number of edges.
In this paper, we show that the maximal number of minimal colourings of a graph with vertices and the chromatic number is equal to , and the single graph for which this bound is attained consists of a -clique and isolated vertices.
In this paper, we give a generalization of a result of Lovasz from [2].
In this paper, we give some results concerning the colouring of the product (cartesian product) of two graphs.
If is a simple graph of size without isolated vertices and is its complement, we show that the domination numbers of and satisfy
where is the minimum degree of vertices in .
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