We prove the conjecture of D. A. Marcus (1981) that every strongly 2-arcconnected directed graph has a directed cycle with at least two chords. As a consequence, every strongly 2-arc-connected directed graph with m arcs has a spanning strong directed subgraph with less than 2 3 m arcs. The constant
Directed cycles with chords
โ Scribed by Marcus, Daniel A.
- Publisher
- John Wiley and Sons
- Year
- 1999
- Tongue
- English
- Weight
- 249 KB
- Volume
- 31
- Category
- Article
- ISSN
- 0364-9024
No coin nor oath required. For personal study only.
โฆ Synopsis
Using a variation of Thomassen's admissible triples technique, we give an alternative proof that every strongly 2-arc-connected directed graph with two or more vertices contains a directed cycle that has at least two chords, while at the same time establishing a more general result.
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