## Abstract It is known that a planar graph on __n__ vertices has branchβwidth/treeβwidth bounded by $\alpha \sqrt {n}$. In many algorithmic applications, it is useful to have a small bound on the constant Ξ±. We give a proof of the best, so far, upper bound for the constant Ξ±. In particular, for th
β¦ LIBER β¦
A new upper bound on the acyclic chromatic indices of planar graphs
β Scribed by Weifan Wang; Qiaojun Shu; Yiqiao Wang
- Book ID
- 118275289
- Publisher
- Elsevier Science
- Year
- 2013
- Tongue
- English
- Weight
- 358 KB
- Volume
- 34
- Category
- Article
- ISSN
- 0195-6698
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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