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
Finding an Oriented Hamiltonian Path in a Tournament
✍ Scribed by Frédéric Havet
- Publisher
- Elsevier Science
- Year
- 2000
- Tongue
- English
- Weight
- 153 KB
- Volume
- 36
- Category
- Article
- ISSN
- 0196-6774
No coin nor oath required. For personal study only.
✦ Synopsis
We present an O n algorithm for finding a specified oriented path of order at Ž 2 . least n in a tournament of order n. Using this algorithm, we present an O n algorithm that finds a specified oriented path from a given vertex if one exists.
📜 SIMILAR VOLUMES
We prove that every tournament of order n 68 contains every oriented Hamiltonian cycle except possibly the directed one when the tournament is reducible.
It is a simple fact that cubic Hamiltonian graphs have at least two Hamiltonian cycles. Finding such a cycle is NP-hard in general, and no polynomial-time algorithm is known for the problem of finding a second Hamiltonian cycle when one such cycle is given as part of the input. We investigate the co
## Abstract An in‐tournament is an oriented graph such that the negative neighborhood of every vertex induces a tournament. Let __m__ = 4 or __m__ = 5 and let __D__ be a strongly connected in‐tournament of order ${{n}}\geq {{2}}{{m}}-{{2}}$ such that each arc belongs to a directed path of order at