We prove that, with some exceptions, every digraph with n 3 9 vertices and at least ( n -1) ( n -2) + 2 arcs contains all orientations of a Hamiltonian cycle.
Oriented hamilton cycles in digraphs
✍ Scribed by Roland Häggkvist; Andrew Thomason
- Publisher
- John Wiley and Sons
- Year
- 1995
- Tongue
- English
- Weight
- 473 KB
- Volume
- 19
- Category
- Article
- ISSN
- 0364-9024
No coin nor oath required. For personal study only.
✦ Synopsis
Abstract
We show that a directed graph of order n will contain n‐cycles of every orientation, provided each vertex has indegree and outdegree at least (1/2 + n^‐1/6^)n and n is sufficiently large. © 1995 John Wiley & Sons, Inc.
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