In this article, we consider the circular chromatic number χ c (G) of series-parallel graphs G. It is well known that series-parallel graphs have chromatic number at most 3. Hence, their circular chromatic numbers are at most 3. If a seriesparallel graph G contains a triangle, then both the chromati
The Determination of the Total Chromatic Number of Series-Parallel Graphs with (G) ≥ 4
✍ Scribed by Shu-Dong Wang; Shan-Chen Pang
- Publisher
- Springer Japan
- Year
- 2005
- Tongue
- English
- Weight
- 126 KB
- Volume
- 21
- Category
- Article
- ISSN
- 0911-0119
No coin nor oath required. For personal study only.
📜 SIMILAR VOLUMES
It was proved by Hell and Zhu that, if G is a series-parallel graph of girth at least 2 (3k -1)/2 , then χ c (G) ≤ 4k/(2k -1). In this article, we prove that the girth requirement is sharp, i.e., for any k ≥ 2, there is a series-parallel graph G of girth 2 (3k -1)/2 -1 such that χ c (G) > 4k/(2k -1)
## Abstract Suppose __G__ is a series‐parallel graph. It was proved in 3 that either ~χ__c__~(__G__) = 3 or ~χ__c__~(__G__) ≤ 8/3. So none of the rationals in the interval (8/3, 3) is the circular chromatic number of a series‐parallel graph. This paper proves that for every rational __r__ ∈ [2, 8/3
In this paper, we shall first prove that for a Halin graph G, 4 °xT (G) °6, where x T (G) is the vertex-face total chromatic number of G. Second, we shall establish a sufficient condition for a Halin graph to have a vertex-face total chromatic number of 6. Finally, we shall give a necessary and suff