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Publication Type : Journal Article
Publisher : Taylor & Francis
Source : AKCE International Journal of Graphs and Combinatorics, 20(3), 339–351. https://doi.org/10.1080/09728600.2023.2187960, 2023
Url : https://www.tandfonline.com/doi/full/10.1080/09728600.2023.2187960
Campus : Coimbatore
School : School of Physical Sciences
Department : Mathematics
Year : 2023
Abstract : 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 [Citation126] and Behzad [Citation6, Citation7] 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 the total coloring of graphs.
Cite this Research Publication : Jayabalan Geetha, Narayanan Narayanan, Kanagasabapathi Somasundaram, "Total colorings-a survey," AKCE International Journal of Graphs and Combinatorics, 20(3), 339–351. https://doi.org/10.1080/09728600.2023.2187960, 2023