An upper bound on the number of planarK-sets
✍ Scribed by János Pach; William Steiger; Endre Szemerédi
- Publisher
- Springer
- Year
- 1992
- Tongue
- English
- Weight
- 746 KB
- Volume
- 7
- Category
- Article
- ISSN
- 0179-5376
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## Abstract We draw the __n__‐dimensional hypercube in the plane with ${5\over 32}4^{n}-\lfloor{{{{n}^{2}+1}\over 2}}\rfloor {2}^{n-2}$ crossings, which improves the previous best estimation and coincides with the long conjectured upper bound of Erdös and Guy. © 2008 Wiley Periodicals, Inc. J Graph
Let G be a simple graph of order n and minimum degree $. The independent domination number i(G) is defined to be the minimum cardinality among all maximal independent sets of vertices of G. In this paper, we show that i(G) n+2$&2 -n$. Thus a conjecture of Favaron is settled in the affirmative.