Total Colourings - A survey
arXiv:1812.05833
Abstract
The smallest integer needed for the assignment of colors to the elements so that the coloring is proper (vertices and edges) is called the total chromatic number of a graph. Vizing and Behzed conjectured that the total coloring can be done using at most colors, where is the maximum degree of . It is not settled even for planar graphs. In this paper we give a survey on total coloring of graphs.
23 pages, 3 figures 1 table