Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4647788 | Discrete Mathematics | 2013 | 5 Pages |
Abstract
While total coloring of graphs and circular coloring of graphs have received a great deal of attention from researchers, there has been a limited amount of work done on circular total colorings. In particular, only a finite number of values a>4 have been realized as the circular total chromatic number of any graph, and it is not yet known whether the set of circular total chromatic numbers of graphs with a given maximum degree r⩾3 is finite or infinite. In this paper, we construct for every integer r⩾3 and every ε>0, a graph with maximum degree râ1 whose circular total chromatic number is in the interval (r,r+ε). This proves that (i) every integer r⩾3 is an accumulation point of the set of circular total chromatic numbers of graphs, and (ii) for every Î⩾2, the set of circular total chromatic numbers of graphs with maximum degree Πis infinite. These results hold also for the set of circular total chromatic numbers of bipartite graphs.
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
M. Ghebleh,