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The total chromatic number of regular graphs of even order and high degree |
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| Authors: | Dezheng Xie Zhongshi He |
| Affiliation: | Department of Mathematics, Chongqing Technology and Business University, Chongqing 400067, China Department of Mathematics, Chongqing University, Chongqing 400041, China |
| Abstract: | The total chromatic number χT(G) of a graph G is the minimum number of colours needed to colour the edges and the vertices of G so that incident or adjacent elements have distinct colours. We show that if G is a regular graph of even order and , thenχT(G)Δ(G)+2. |
| Keywords: | Total chromatic number Total colouring Total colouring conjecture |
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