Total colorings-a survey

The 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 presented.) colors, where (Formula presented.) 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.