
Accession Number : AD0708421
Title : DISCONNECTEDCOLORINGS OF GRAPHS.
Descriptive Note : Technical rept.,
Corporate Author : IOWA UNIV IOWA CITY DEPT OF MATHEMATICS
Personal Author(s) : Hedetniemi,Stephen T.
Report Date : JUN 1970
Pagination or Media Count : 35
Abstract : A disconnectedcoloring (or Dcoloring) of a graph G = (V,E) is a partition pi = V1,V2,...,Vn of V such that for every i, the subgraph induced by the subset Vi is disconnected. The Dchromatic number Chi sub d (G) of G is the smallest number of color classes (subsets) in any Dcoloring of G. This paper contains a large variety of results for Dcolorings and Chi sub d which are very similar to corresponding results that have been established for the traditional colorings and chromatic number Chi(g) of graphs; in particular, analogs are given for established results on (1) bounds for the chromatic and achromatic number, (2) colorings of planar graphs, (3) critical graphs, (4) the linechromatic number, and (v) uniquelycolorable graphs. These new results indicate that the established results reveal much less about properties of colorings than they do about concepts which are much more general. They also reveal that most of the established results on coloring are really very simple. One conclusion that can be drawn from this is that one has not learned very much yet about the concept of coloring a graph. Another conclusion is that there is now emerging a new theory of partitions of graphs of which the theory of colorings is but a part. (Author)
Descriptors : (*GRAPHICS, COMBINATORIAL ANALYSIS), SET THEORY, COLORS, THEOREMS
Subject Categories : Theoretical Mathematics
Distribution Statement : APPROVED FOR PUBLIC RELEASE