𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Bounds on chromatic numbers of multiple factors of a complete graph

✍ Scribed by Ján Plesník

Publisher
John Wiley and Sons
Year
1978
Tongue
English
Weight
306 KB
Volume
2
Category
Article
ISSN
0364-9024

No coin nor oath required. For personal study only.

✦ Synopsis

Abstract

Bounds on the sum and product of the chromatic numbers of n factors of a complete graph of order p are shown to exist. The well‐known theorem of Nordhaus and Gaddum solves the problem for n = 2. Strict lower and some upper bounds for any n and strict upper bounds for n = 3 are given. In particular, the sum of the chromatic numbers of three factors is between 3__p__^1/3^ and p + 3 and the product is between p and [(p + 3)/3]^3^.

📜 SIMILAR VOLUMES

Bounds for the harmonious chromatic numb
Bounds for the harmonious chromatic number of a graph
✍ I. Krasikov; Y. Roditty 📂 Article 📅 1994 🏛 John Wiley and Sons 🌐 English ⚖ 231 KB 👁 2 views

## Abstract The upper bound for the harmonious chromatic number of a graph given by Zhikang Lu and by C. McDiarmid and Luo Xinhua, independently (__Journal of Graph Theory__, 1991, pp. 345–347 and 629–636) and the lower bound given by D. G. Beane, N. L. Biggs, and B. J. Wilson (__Journal of Graph T

Improved bounds for the chromatic number
Improved bounds for the chromatic number of a graph
✍ S. Louis Hakimi; Edward Schmeichel 📂 Article 📅 2004 🏛 John Wiley and Sons 🌐 English ⚖ 97 KB 👁 2 views

## Abstract After giving a new proof of a well‐known theorem of Dirac on critical graphs, we discuss the elegant upper bounds of Matula and Szekeres‐Wilf which follow from it. In order to improve these bounds, we consider the following fundamental coloring problem: given an edge‐cut (__V__~1~, __V_

New bounds for the chromatic number of g
New bounds for the chromatic number of graphs
✍ Manouchehr Zaker 📂 Article 📅 2008 🏛 John Wiley and Sons 🌐 English ⚖ 184 KB 👁 1 views

## Abstract In this article we first give an upper bound for the chromatic number of a graph in terms of its degrees. This bound generalizes and modifies the bound given in 11. Next, we obtain an upper bound of the order of magnitude ${\cal O}({n}^{{1}-\epsilon})$ for the coloring number of a graph

Total chromatic number of complete r-par
Total chromatic number of complete r-partite graphs
✍ K. H. Chew; H. P. Yap 📂 Article 📅 1992 🏛 John Wiley and Sons 🌐 English ⚖ 284 KB 👁 1 views

## Abstract Rosenfeld (1971) proved that the Total Colouring Conjecture holds for balanced complete __r__‐partite graphs. Bermond (1974) determined the exact total chromatic number of every balanced complete __r__‐partite graph. Rosenfeld's result had been generalized recently to complete __r__‐par

Upper Bounds of Entire Chromatic Number
Upper Bounds of Entire Chromatic Number of Plane Graphs
✍ W. Weifan 📂 Article 📅 1999 🏛 Elsevier Science 🌐 English ⚖ 35 KB

The entire chromatic number χ ve f (G) of a plane graph G is the least number of colors assigned to the vertices, edges and faces so that every two adjacent or incident pair of them receive different colors. conjectured that χ ve f (G) ≤ + 4 for every plane graph G. In this paper we prove the conj