✦ LIBER ✦

The fractional chromatic number of infinite graphs

✍ Scribed by Imre Leader

Publisher: John Wiley and Sons
Year: 1995
Tongue: English
Weight: 398 KB
Volume: 20
Category: Article
ISSN: 0364-9024
DOI: 10.1002/jgt.3190200404

No coin nor oath required. For personal study only.

✦ Synopsis

Abstract

The fractional chromatic number of a graph G is the infimum of the total weight that can be assigned to the independent sets of G in such a way that, for each vertex v of G, the sum of the weights of the independent sets containing v is at least 1.

In this note we give a graph a graph whose fractional chromatic number is strictly greater than the supremum of the fractional chromatic numbers of its finite subgraphs. This answers a question of Zhu. We also give some grphs for which the fractional chromatic number is not attined, answering another of Zhu. © 1995 John Wiley & Sons, Inc.

📜 SIMILAR VOLUMES

The fractional chromatic number of mycie

The fractional chromatic number of mycielski's graphs

✍ Michael Larsen; James Propp; Daniel Ullman 📂 Article 📅 1995 🏛 John Wiley and Sons 🌐 English ⚖ 236 KB

The most familiar construction of graphs whose clique number is much smaller than their chromatic number is due to Mycielski, who constructed a sequence G, of triangle-free graphs with ,y(G,) = n. In this article, w e calculate the fractional chromatic number of G, and show that this sequence of num

Circular Chromatic Numbers and Fractiona

Circular Chromatic Numbers and Fractional Chromatic Numbers of Distance Graphs

✍ G.J. Chang; L. Huang; X. Zhu 📂 Article 📅 1998 🏛 Elsevier Science 🌐 English ⚖ 171 KB

This paper studies circular chromatic numbers and fractional chromatic numbers of distance graphs G(Z , D) for various distance sets D. In particular, we determine these numbers for those D sets of size two, for some special D sets of size three, for

Girth and fractional chromatic number of

Girth and fractional chromatic number of planar graphs

✍ Amir Pirnazar; Daniel H. Ullman 📂 Article 📅 2002 🏛 John Wiley and Sons 🌐 English ⚖ 152 KB 👁 1 views

## Abstract In 1959, even before the Four‐Color Theorem was proved, Grötzsch showed that planar graphs with girth at least 4 have chromatic number at the most 3. We examine the fractional analogue of this theorem and its generalizations. For any fixed girth, we ask for the largest possible fraction

Fractional chromatic numbers of cones ov

Fractional chromatic numbers of cones over graphs

✍ Claude Tardif 📂 Article 📅 2001 🏛 John Wiley and Sons 🌐 English ⚖ 95 KB 👁 1 views

## Abstract We introduce a construction called the __cone__ over a graph. It is a natural generalisation of Mycielski's construction. We give a formula for the fractional chromatic numbers of all cones over graphs, which generalizes that given in 3 for Mycielski's construction. © 2001 John Wiley &

Fractional chromatic number and circular

Fractional chromatic number and circular chromatic number for distance graphs with large clique size

✍ Daphne Der-Fen Liu; Xuding Zhu 📂 Article 📅 2004 🏛 John Wiley and Sons 🌐 English ⚖ 136 KB

## Abstract An Erratum has been published for this article in Journal of Graph Theory 48: 329–330, 2005. Let __M__ be a set of positive integers. The distance graph generated by __M__, denoted by __G__(__Z, M__), has the set __Z__ of all integers as the vertex set, and edges __ij__ whenever |__i__

The chromatic number of oriented graphs

✍ Sopena, Eric 📂 Article 📅 1997 🏛 John Wiley and Sons 🌐 English ⚖ 198 KB 👁 2 views

We introduce in this paper the notion of the chromatic number of an oriented graph G (that is of an antisymmetric directed graph) defined as the minimum order of an oriented graph H such that G admits a homomorphism to H. We study the chromatic number of oriented k-trees and of oriented graphs with