Total colorings-a survey

Abstract

AbstractThe smallest integer k needed for the assignment of k colors to the elements so that the coloring is proper (vertices and edges) is called the total chromatic number of a graph. Vizing [126] and Behzad [6, 7] conjectured that the total coloring can be done using at most [Formula: see text] colors, where [Formula: see text] is the maximum degree of G. It is not settled even for planar graphs. In this paper, we give a survey on the total coloring of graphs.

Keywords

• Total coloring
• survey
• planar graph
• product graphs
• non-planar graphs