✦ LIBER ✦
Meyniel's theorem for strongly (p, q) - Hamiltonian digraphs
✍ Scribed by A. P. Wojda
- Publisher
- John Wiley and Sons
- Year
- 1981
- Tongue
- English
- Weight
- 134 KB
- Volume
- 5
- Category
- Article
- ISSN
- 0364-9024
No coin nor oath required. For personal study only.
✦ Synopsis
Abstract
We give the following theorem: Let D = (V, E) be a strongly (p + q + 1)‐connected digraph with n ≥ p + q + 1 vertices, where p and q are nonnegative integers, p ≤ n ‐ 2, n ≥ 2. Suppose that, for each four vertices u, v, w, z (not necessarily distinct) such that {u, v} ∩ {w, z} = Ø, (w, u) ∉ E, (v, z) ∉ E, we have id(u) + od(v) + od(w + id(z) ≥ 2 (n + p + q)) + 1. Then D is strongly (p, q)‐Hamiltonian.