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.

Note on Turán's graph

Dănuţ Marcu — 1993

Czechoslovak Mathematical Journal

On colouring products of graphs

Dănuţ Marcu — 1996

Mathematica Bohemica

In this paper, we give some results concerning the colouring of the product (cartesian product) of two graphs.

Note on a Lovász's result

Dănuţ Marcu — 1997

Mathematica Bohemica

In this paper, we give a generalization of a result of Lovasz from [2].

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 $\bar{G}$ is its complement, we show that the domination numbers of $G$ and $\bar{G}$ satisfy $γ (G) + γ (\bar{G}) \leq \}\begin{matrix} n - δ + 2 if γ (G) > 3, δ + 3 if γ (\bar{G}) > 3, \end{matrix}$ where $δ$ is the minimum degree of vertices in $G$ .

Note on the Circuits of a Perfect Matroid Design

Danut Marcu — 1984

Publications de l'Institut Mathématique

A Note on a Bermond's Conjecture

Danut Marcu — 1986

Publications de l'Institut Mathématique

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