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arXiv · 1812.05833

Total Colourings - A survey

Geetha Jayabalan·Narayanan N·K Somasundaram
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Abstract

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.

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Geetha Jayabalan, Narayanan N, K Somasundaram. 2018-12-14. Total Colourings - A survey. https://arxiv.org/abs/1812.05833

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