Colour Classes for r-Graphs

Abstract

By anr-graph G we mean a finite setV(G) of elements called vertices and a setE(G) of some of ther-subsets ofV(G) called edges. This paper defines certain colour classes ofr-graphs which connect the material of a variety of recent graph theoretic literature in that many existing results may be reformulated as structural properties of the classes for some special cases ofr-graphs. It is shown that the concepts of Ramsey Numbers, chromatic number and index may be defined in terms of these classes. These concepts and some of their properties are generalized. The final subsection compares two existing bounds for the chromatic number of a graph.