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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 χt(G). The Total Coloring Conjecture (TCC) states that for every simple graph G, Δ(G)+1χt(G)Δ(G)+2. G is called Type 1 (resp. Type 2) if χt(G)=Δ(G)+1 (resp. χt(G)=Δ(G)+2). In this paper, we prove that the generalized Mycielski graphs satisfy TCC. Furthermore, we get that if Δ(G)|V(G)|12, then the generalized Mycielski graph μm(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

Citer

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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