On the Set of Circular Total Chromatic Numbers of Graphs
Abstract
For every integer r3 and every >0 we construct a graph with maximum degree r-1 whose circular total chromatic number is in the interval (r,r+). This proves that (i) every integer r3 is an accumulation point of the set of circular total chromatic numbers of graphs, and (ii) for every 2, the set of circular total chromatic numbers of graphs with maximum degree is infinite. All these results hold for the set of circular total chromatic numbers of bipartite graphs as well.
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