𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Parity of paths and circuits in tournaments

✍ Scribed by Rodney Forcade

Publisher
Elsevier Science
Year
1973
Tongue
English
Weight
393 KB
Volume
6
Category
Article
ISSN
0012-365X

No coin nor oath required. For personal study only.

πŸ“œ SIMILAR VOLUMES

Endpoint extendable paths in tournaments
Endpoint extendable paths in tournaments
✍ Faudree, Ralph J.; GyοΏ½rfοΏ½s, AndrοΏ½s πŸ“‚ Article πŸ“… 1996 πŸ› John Wiley and Sons 🌐 English βš– 254 KB

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.

Parity theorems for paths and cycles in
Parity theorems for paths and cycles in graphs
✍ J. A. Bondy; F. Y. Halberstam πŸ“‚ Article πŸ“… 1986 πŸ› John Wiley and Sons 🌐 English βš– 294 KB πŸ‘ 1 views

We extend an elegant proof technique of A . G . Thomason, and deduce several parity theorems for paths and cycles in graphs. For example, a graph in which each vertex is of even degree has an even number of paths if and only if it is of even order, and a graph in which each vertex is of odd degree h

Oriented Hamiltonian Paths in Tournament
Oriented Hamiltonian Paths in Tournaments: A Proof of Rosenfeld's Conjecture
✍ FrΓ©dΓ©ric Havet; StΓ©phan ThomassΓ© πŸ“‚ Article πŸ“… 2000 πŸ› Elsevier Science 🌐 English βš– 284 KB

We prove that with three exceptions, every tournament of order n contains each oriented path of order n. The exceptions are the antidirected paths in the 3-cycle, in the regular tournament on 5 vertices, and in the Paley tournament on 7 vertices. ## 2000 Academic Press Tournaments are very rich st