Path-connectivity in local tournaments
β Scribed by Yubao Guo
- Publisher
- Elsevier Science
- Year
- 1997
- Tongue
- English
- Weight
- 998 KB
- Volume
- 167-168
- Category
- Article
- ISSN
- 0012-365X
No coin nor oath required. For personal study only.
β¦ Synopsis
A digraph T is called a local tournament if for every vertex x of T, the set of in-neighbors as well as the set of out-neighbors of x induce tournaments. We give characterizations of generalized arc-pancyclic and strongly path-panconnected local tournaments, respectively. Our results generalize those due to Bu and Zhang (1996) about arc-pancyclic local tournaments and about strongly arc-pancyclic local tournaments, respectively. Moreover, these also extend the corresponding results in Tian et al. (1982) and Zhang (1982) for tournaments.
π SIMILAR VOLUMES
## Abstract A __tournament__ is an orientation of the edges of a complete graph. An arc is __pancyclic__ in a tournament __T__ if it is contained in a cycle of length __l__, for every 3ββ€β__l__ββ€β|T|. Let __p__(__T__) denote the number of pancyclic arcs in a tournament __T__. In 4, Moon showed that
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.