✦ LIBER ✦

Inequalities between the domination number and the chromatic number of a graph

✍ Scribed by Dieter Gernert

Publisher: Elsevier Science
Year: 1989
Tongue: English
Weight: 230 KB
Volume: 76
Category: Article
ISSN: 0012-365X
DOI: 10.1016/0012-365x(89)90308-7

No coin nor oath required. For personal study only.

✦ Synopsis

Upper bounds for u + x and ax are proved, where u is the domination number and x the chromatic number of a graph.

📜 SIMILAR VOLUMES

Some inequalities on the chromatic numbe

Some inequalities on the chromatic number of a graph

✍ T. King; G.L. Nemhauser 📂 Article 📅 1974 🏛 Elsevier Science 🌐 English ⚖ 567 KB

Some upper bounds for the product of the

Some upper bounds for the product of the domination number and the chromatic number of a graph

✍ Jerzy Topp; Lutz Volkmann 📂 Article 📅 1993 🏛 Elsevier Science 🌐 English ⚖ 199 KB

Topp, J. and L. Volkmann, Some upper bounds for the product of the domination number and the chromatic number of a graph, Discrete Mathematics 118 (1993) 2899292. Some new upper bounds for yx are proved, where y is the domination number and x is the chromatic number of a graph. All graphs consider

The star chromatic number of a graph

✍ H. L. Abbott; B. Zhou 📂 Article 📅 1993 🏛 John Wiley and Sons 🌐 English ⚖ 469 KB 👁 2 views

## Abstract We study a generalization of the notion of the chromatic number of a graph in which the colors assigned to adjacent vertices are required to be, in a certain sense, far apart. © 1993 John Wiley & Sons, Inc.

The chromatic covering number of a graph

✍ Reza Naserasr; Claude Tardif 📂 Article 📅 2006 🏛 John Wiley and Sons 🌐 English ⚖ 72 KB 👁 2 views

Following [1] , we investigate the problem of covering a graph G with induced subgraphs G 1 ; . . . ; G k of possibly smaller chromatic number, but such that for every vertex u of G, the sum of reciprocals of the chromatic numbers of the G i 's containing u is at least 1. The existence of such ''ch

Estimations for the domination number of

Estimations for the domination number of a graph

✍ Peter Flach; Lutz Volkmann 📂 Article 📅 1990 🏛 Elsevier Science 🌐 English ⚖ 345 KB

On the r-domination number of a graph

✍ Jerrold R. Griggs; Joan P. Hutchinson 📂 Article 📅 1992 🏛 Elsevier Science 🌐 English ⚖ 468 KB

For r > 0, let the r-domination number of a graph, d,, be the size of a smallest set of vertices such that every vertex of the graph is within distance r of a vertex in that set. This paper contains proofs that every graph with a spanning tree with at least n/2 leaves has d, s n/(2r); this compares