An upper bound on the sum of powers of the degrees of simple 1-planar graphs
✍ Scribed by Czap, Július; Harant, Jochen; Hudák, Dávid
- Book ID
- 122736552
- Publisher
- Elsevier Science
- Year
- 2014
- Tongue
- English
- Weight
- 220 KB
- Volume
- 165
- Category
- Article
- ISSN
- 0166-218X
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📜 SIMILAR VOLUMES
Let G be a simple graph with n vertices, e edges and vertex degrees &, d2 ..... d~. It is proved that d2+ ... +d~<~e(2e/(n-1)+ n-2) when n~>2. This bound does not generalize to all sequences of positive integers. A comparison is made to another upper bound on d 2 +. • -+ d 2, due to Sz6kely et al. (
graphs is at most log, 6.
## Abstract It is known that a planar graph on __n__ vertices has branch‐width/tree‐width bounded by $\alpha \sqrt {n}$. In many algorithmic applications, it is useful to have a small bound on the constant α. We give a proof of the best, so far, upper bound for the constant α. In particular, for th