Total Colourings - A survey

12/14/2018

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by   Geetha Jayabalan, et al.

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The smallest integer k 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 Δ(G)+2 colors, where Δ(G) is the maximum degree of G. It is not settled even for planar graphs. In this paper we give a survey on total coloring of graphs.