✦ LIBER ✦

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

✍ Scribed by Zhishi Pan; Xuding Zhu

Book ID: 108315650
Publisher: Elsevier Science
Year: 2002
Tongue: English
Weight: 115 KB
Volume: 245
Category: Article
ISSN: 0012-365X
DOI: 10.1016/s0012-365x(01)00144-3

No coin nor oath required. For personal study only.

📜 SIMILAR VOLUMES

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)

The circular chromatic number of series-

The circular chromatic number of series-parallel graphs

✍ Hell, Pavol; Zhu, Xuding 📂 Article 📅 2000 🏛 John Wiley and Sons 🌐 English ⚖ 238 KB 👁 2 views

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

Density of the circular chromatic number

Density of the circular chromatic numbers of series-parallel graphs

✍ Zhishi Pan; Xuding Zhu 📂 Article 📅 2004 🏛 John Wiley and Sons 🌐 English ⚖ 120 KB 👁 1 views

## 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

List edge chromatic number of graphs wit

List edge chromatic number of graphs with large girth

✍ A.V. Kostochka 📂 Article 📅 1992 🏛 Elsevier Science 🌐 English ⚖ 785 KB

Kostochka, A.V., List edge chromatic number of graphs with large girth, Discrete Mathematics 101 (1992) 189-201. It is shown that the list edge chromatic number of any graph with maximal degree A and girth at least 8A(ln A + 1.1) is equal to A + 1 or to A. Conjecture 1. The list edge chromatic numbe

The circular chromatic index of graphs o

The circular chromatic index of graphs of high girth

✍ Tomáš Kaiser; Daniel Král'; Riste Škrekovski; Xuding Zhu 📂 Article 📅 2007 🏛 Elsevier Science 🌐 English ⚖ 162 KB

On the circular chromatic number of circ

On the circular chromatic number of circular partitionable graphs

✍ Arnaud Pêcher; Xuding Zhu 📂 Article 📅 2006 🏛 John Wiley and Sons 🌐 English ⚖ 168 KB

## Abstract This article studies the circular chromatic number of a class of circular partitionable graphs. We prove that an infinite family of circular partitionable graphs __G__ has $\chi\_ c (G) = \chi(G)$. A consequence of this result is that we obtain an infinite family of graphs __G__ with th