An Extremal Problem For Random Graphs And The Number Of Graphs With Large Even-Girth

The circular chromatic number of series-

The circular chromatic number of series-parallel graphs with large girth

✍ Chien, Chihyun; Zhu, Xuding 📂 Article 📅 2000 🏛 John Wiley and Sons 🌐 English ⚖ 213 KB 👁 2 views

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)