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Note on graphs colouring

Dănuţ Marcu — 1992

Mathematica Bohemica

In this paper, we show that the maximal number of minimal colourings of a graph with n vertices and the chromatic number k is equal to k n - k , and the single graph for which this bound is attained consists of a k -clique and n - k isolated vertices.

Note on k -chromatic graphs

Dănuţ Marcu — 1994

Mathematica Bohemica

In this paper we characterize k -chromatic graphs without isolated vertices and connected k -chromatic graphs having a minimal number of edges.

A note on the domination number of a graph and its complement

Dănuţ Marcu — 2001

Mathematica Bohemica

If G is a simple graph of size n without isolated vertices and G ¯ is its complement, we show that the domination numbers of G and G ¯ satisfy γ ( G ) + γ ( G ¯ ) n - δ + 2 if γ ( G ) > 3 , δ + 3 if γ ( G ¯ ) > 3 , where δ is the minimum degree of vertices in G .

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