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Article Dans Une Revue Discrete Mathematics Année : 2014

Total chromatic number of generalized Mycielski graphs

Résumé

A total coloring of a simple graph $G$ is a coloring of both the edges and the vertices. A total coloring is proper if no two adjacent or incident elements reveive the same color. The minimum number of colors required for a proper total coloring of $G$ is called the total chromatic number of $G$ and denoted by $\chi_{t}(G)$. The Total Coloring Conjecture (TCC) states that for every simple graph $G$, $\Delta(G)+1\leq \chi_{t}(G)\leq \Delta(G)+2$. $G$ is called Type 1 (resp. Type 2) if $\chi_{t}(G)=\Delta(G)+1$ (resp. $\chi_{t}(G)=\Delta(G)+2$). In this paper, we prove that the generalized Mycielski graphs satisfy TCC. Furthermore, we get that if $\Delta(G)\leq \frac{|V(G)|-1}{2}$, then the generalized Mycielski graph $\mu_{m}(G)$ is Type 1.
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Dates et versions

hal-01132240 , version 1 (16-03-2015)

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  • HAL Id : hal-01132240 , version 1

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Meirun Chen, Xiaofeng Guo, Hao Li, Lianzhu Zhang. Total chromatic number of generalized Mycielski graphs. Discrete Mathematics, 2014, pp.48-51. ⟨hal-01132240⟩
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