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Total Colourings - A survey

Combinatorics 2018-12-17 v1 Discrete Mathematics

Abstract

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

Keywords

Cite

@article{arxiv.1812.05833,
  title  = {Total Colourings - A survey},
  author = {Geetha Jayabalan and Narayanan N and K Somasundaram},
  journal= {arXiv preprint arXiv:1812.05833},
  year   = {2018}
}

Comments

23 pages, 3 figures 1 table

R2 v1 2026-06-23T06:42:22.829Z