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Zbl 1190.05064
Bode, Jens-P.; Kemnitz, Arnfried; Klages, Rebecca
Circular total colorings of some type-2 graphs.
(English)
[J] Congr. Numerantium 189, 129-137 (2008). ISSN 0384-9864

Summary: A $(k, d$-total coloring$(k,d\in\Bbb N$, $k \ge 2d)$ of a graph $G$ is an assignment $c$ of colors $\{0,1,\dots,k-1\}$ to the vertices and edges of $G$ such that $d\le|c(x)-c(x')|\le k-d$ whenever $x$ and $x'$ are adjacent or incident. The circular total chromatic number $\chi_c''(G)$ is defined by $\chi_c''(G) =\inf\{k/d : G$ admits a $(k,d)$-total coloring\}. We present some infinite classes of graphs $G$ such that $\chi_c''(G)$ is strictly less than the total chromatic number $\chi''(G)$.
MSC 2000:
*05C15 Chromatic theory of graphs and maps

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