A graph G with maximum degree and edge chromatic number (G)> is edge--critical if (G -e) = for every edge e of G. It is proved here that the vertex independence number of an edge--critical graph of order n is less than 3 5 n. For large , this improves on the best bound previously known, which was ro
Bounds for the matching number, the edge chromatic number and the independence number of a graph in terms of rank
β Scribed by Wang, Long; Wong, Dein
- Book ID
- 122197585
- Publisher
- Elsevier Science
- Year
- 2014
- Tongue
- English
- Weight
- 372 KB
- Volume
- 166
- Category
- Article
- ISSN
- 0166-218X
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
In 1968, Vizing conjectured that if G is a -critical graph with n vertices, then (G) β€ n / 2, where (G) is the independence number of G. In this paper, we apply Vizing and Vizing-like adjacency lemmas to this problem and prove that (G)<(((5 -6)n) / (8 -6))<5n / 8 if β₯ 6. α§ 2010 Wiley
## 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. 345β347 and 629β636) and the lower bound given by D. G. Beane, N. L. Biggs, and B. J. Wilson (__Journal of Graph T
## Abstract After giving a new proof of a wellβknown theorem of Dirac on critical graphs, we discuss the elegant upper bounds of Matula and SzekeresβWilf which follow from it. In order to improve these bounds, we consider the following fundamental coloring problem: given an edgeβcut (__V__~1~, __V_
We show that if the adjacency matrix of a graph X has 2-rank 2r, then the chromatic number of X is at most 2 r +1, and that this bound is tight. 2001