Let s(n) be the threshold for which each directed path of order smaller than s ( n ) is extendible from one of its endpoints in some tournament T,. It is shown that s(n) is asymptotic to 3n/4, with an error term at most 3 for infinitely many n. There are six tournaments with s ( n ) = n.
β¦ LIBER β¦
Endpoint extendable paths in dense graphs
β Scribed by Guantao Chen; Zhiquan Hu; Hao Li
- Book ID
- 113567449
- Publisher
- Elsevier Science
- Year
- 2012
- Tongue
- English
- Weight
- 266 KB
- Volume
- 312
- Category
- Article
- ISSN
- 0012-365X
No coin nor oath required. For personal study only.
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Let G be a connected graph with p vertices and n a positive integer with 1 dn <(p/2) -1. G is said to be O-extendable if G has a perfect matching. G is said to be n-extendable if G has a matching of size n and every matching of size n in G extends to (i.e. is a subset of) a perfect matching. It is s