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Inclusion total chromatic number
Discrete Mathematics ( IF 0.7 ) Pub Date : 2021-06-11 , DOI: 10.1016/j.disc.2021.112489
Jakub Kwaśny

Let G=(V,E) be a graph and c:(VE)C be a proper total colouring of G, where C is a set of colours. We call c inclusion-free if for each vertex, the set of colours appearing on the vertex and the incident edges is not a subset of the respective sets of its neighbours. With a probabilistic argument we show that the minimum number of colours for inclusion-free total colouring, denoted by χ(G), is bounded from above by Δ+150logΔ for any graph G with large enough maximum degree Δ. Then we prove that χ(G)6 for any subcubic graph G, which meets the bound for adjacent vertex distinguishing total colouring.



中文翻译:

包含总色数

G=(,) 是一个图形和 C()CG的适当总着色,其中C是一组颜色。如果对于每个顶点,出现在顶点和入射边上的颜色集不是其相邻的相应集的子集,我们称c为无包含。通过概率论,我们证明了无夹杂总着色的最小颜色数,表示为χ(G), 由上界 Δ+150日志Δ对于任何具有足够大的最大度 Δ 的图G。然后我们证明χ(G)6对于任何亚立方图G,它满足相邻顶点区分总着色的界限。

更新日期:2021-06-13
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