On the Set of Circular Total Chromatic Numbers of Graphs

Abstract

For every integer $r\ge 3$ 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 $r\ge 3$ is an accumulation point of the set of circular total chromatic numbers of graphs, and (ii) for every $\Delta \ge 2$, the set of circular total chromatic numbers of graphs with maximum degree $\Delta$ is infinite. All these results hold for the set of circular total chromatic numbers of bipartite graphs as well.

References in corpus (2)

• Circular chromatic index of graphs of maximum degree 3
• Circular edge-colorings of cubic graphs with girth six