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arXiv · 1106.0017

On the Set of Circular Total Chromatic Numbers of Graphs

Mohammad Ghebleh
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Abstract

For every integer $r\ge3$ and every $\eps>0$ we construct a graph with maximum degree $r-1$ whose circular total chromatic number is in the interval $(r,r+\eps)$. This proves that (i) every integer $r\ge3$ is an accumulation point of the set of circular total chromatic numbers of graphs, and (ii) for every $Δ\ge2$, the set of circular total chromatic numbers of graphs with maximum degree $Δ$ is infinite. All these results hold for the set of circular total chromatic numbers of bipartite graphs as well.

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Mohammad Ghebleh. 2011-05-31. On the Set of Circular Total Chromatic Numbers of Graphs. https://doi.org/10.1016/j.disc.2012.10.023

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