𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Improvement on Brooks' chromatic bound for a class of graphs

✍ Scribed by Medha Dhurandhar


Book ID
107748395
Publisher
Elsevier Science
Year
1982
Tongue
English
Weight
547 KB
Volume
42
Category
Article
ISSN
0012-365X

No coin nor oath required. For personal study only.


πŸ“œ SIMILAR VOLUMES


Note on Choudum's β€œchromatic bounds for
✍ Medha Javdekar πŸ“‚ Article πŸ“… 1980 πŸ› John Wiley and Sons 🌐 English βš– 105 KB

## Abstract If a graph __G__ has no induced subgraph isomorphic to __K__~1,3β€²~ __K__~5~‐__e__, or a third graph that can be selected from two specific graphs, then the chromatic number of __G__ is either __d__ or __d__ + 1, where __d__ is the maximum order of a clique in __G__.

Improved bounds for the chromatic number
✍ S. Louis Hakimi; Edward Schmeichel πŸ“‚ Article πŸ“… 2004 πŸ› John Wiley and Sons 🌐 English βš– 97 KB πŸ‘ 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_

Improved bounds for the chromatic index
✍ Hakimi, S. Louis; Schmeichel, Edward F. πŸ“‚ Article πŸ“… 1999 πŸ› John Wiley and Sons 🌐 English βš– 321 KB πŸ‘ 2 views

We show that coloring the edges of a multigraph G in a particular order often leads to improved upper bounds for the chromatic index Ο‡ (G). Applying this to simple graphs, we significantly generalize recent conditions based on the core of G (i.e., the subgraph of G induced by the vertices of degree

A bound for the game chromatic number of
✍ Thomas Dinski; Xuding Zhu πŸ“‚ Article πŸ“… 1999 πŸ› Elsevier Science 🌐 English βš– 580 KB

We show that if a graph has acyclic chromatic number k, then its game chromatic number is at most k(k + 1). By applying the known upper bounds for the acyclic chromatic numbers of various classes of graphs, we obtain upper bounds for the game chromatic number of these classes of graphs. In particula

A bound on the chromatic number of a gra
✍ Paul A. Catlin πŸ“‚ Article πŸ“… 1978 πŸ› Elsevier Science 🌐 English βš– 392 KB

We give an upper bound on the chromatic number of a graph in terms of its maximum degree and the size of the largest complete subgraph. Our result extends a theorem due to i3rook.s.