On the Set of Circular Total Chromatic Numbers of Graphs

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 $\Delta\ge2$, 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

Efficient Enumeration of Maximal k-Degenerate Subgraphs in a Chordal Graph

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