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An improved upper bound on the number of intersections between two rectangular paths

✍ Scribed by Kim-Heng Teo; Tai-Ching Tuan


Book ID
107765973
Publisher
Elsevier Science
Year
1991
Tongue
English
Weight
572 KB
Volume
37
Category
Article
ISSN
0020-0190

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πŸ“œ SIMILAR VOLUMES


An improved upper bound on the crossing
✍ Luerbio Faria; Celina Miraglia Herrera de Figueiredo; Ondrej SΓ½kora; Imrich Vrt' πŸ“‚ Article πŸ“… 2008 πŸ› John Wiley and Sons 🌐 English βš– 288 KB

## 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 ErdΓΆs and Guy. Β© 2008 Wiley Periodicals, Inc. J Graph

An upper bound for the path number of a
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## Abstract The path number of a graph __G__, denoted __p(G)__, is the minimum number of edge‐disjoint paths covering the edges of __G.__ LovΓ‘sz has proved that if __G__ has __u__ odd vertices and __g__ even vertices, then __p(G)__ ≀ 1/2 __u__ + __g__ ‐ 1 ≀ __n__ ‐ 1, where __n__ is the total numbe