Corpus ID: 214612278

A proof of the Total Coloring Conjecture

@article{Murthy2020APO,
  title={A proof of the Total Coloring Conjecture},
  author={T. Srinivasa Murthy},
  journal={ArXiv},
  year={2020},
  volume={abs/2003.09658}
}
  • T. Murthy
  • Published 2020
  • Mathematics, Computer Science
  • ArXiv
A $total\ coloring$ of a graph G is a map $f:V(G) \cup E(G) \rightarrow \mathcal{K}$, where $\mathcal{K}$ is a set of colors, satisfying the following three conditions: 1. $f(u) \neq f(v)$ for any two adjacent vertices $u, v \in V(G)$; 2. $f(e) \neq f(e')$ for any two adjacent edges $e, e' \in E(G)$; and 3. $f(v) \neq f(e)$ for any vertex $v \in V(G)$ and any edge $e \in E(G)$ that is incident to same vertex $v$. The $total\ chromatic\ number$, $\chi''(G)$, is the minimum number of colors… Expand
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