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)
The circular chromatic index of graphs of high girth
✍ Scribed by Tomáš Kaiser; Daniel Král'; Riste Škrekovski; Xuding Zhu
- Book ID
- 108167406
- Publisher
- Elsevier Science
- Year
- 2007
- Tongue
- English
- Weight
- 162 KB
- Volume
- 97
- Category
- Article
- ISSN
- 0095-8956
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