Contains a wealth of information previously scattered in research journals, conference
proceedings and technical reports. Identifies more than 200 unsolved problems. Every …

In 1956, Nordhaus and Gaddum gave lower and upper bounds on the sum and the product
of the chromatic number of a graph and its complement, in terms of the order of the graph …

This is the seventh edition of a quarterly column the purpose of which is to provide
continuing coverage of new developments in the theory of NP-completeness. The …

It is the origin of the Four Color Problem by Francis Guthrie in 1852 that led to coloring maps
and then to coloring planar graphs—not only coloring its regions but coloring its vertices and …

The harmonious chromatic number of a graph is the least number of colours in a vertex
colouring such that each pair of colours appears on at most one edge. The achromatic …

A harmonious colouring of a simple graph G is a proper vertex colouring such that each pair
of colours appears together on at most one edge. The harmonious chromatic number h (G) …

Let G be a simple graph. The achromatic number ψ (G) is the largest number of colors
possible in a proper vertex coloring of G in which each pair of colors is adjacent somewhere …

Hopcroft and Krishnamoorthy (1983) have shown that the harmonious coloring problem is
NP-complete, introducing the notion of a harmonious coloring of a graph as being a vertex …

The interest in edge colorings of graphs can be traced back to 1880 when the Scottish
mathematician Peter Guthrie Tait attempted to solve the Four Color Problem with the aid of …

A proper total colouring of a graph $ G $ is called harmonious if it has the further property
that when replacing each unordered pair of incident vertices and edges with their colours …