Random Edge Augmentation for Hamiltonian Cycle Powers
Research Paper#Graph Theory, Random Graphs, Hamiltonian Cycles🔬 Research|Analyzed: Jan 3, 2026 18:25•
Published: Dec 29, 2025 22:24
•1 min read
•ArXivAnalysis
This paper investigates the number of random edges needed to ensure the existence of higher powers of Hamiltonian cycles in a specific type of graph (Pósa-Seymour graphs). The research focuses on determining thresholds for this augmentation process, particularly the 'over-threshold', and provides bounds and specific results for different parameters. The work contributes to the understanding of graph properties and the impact of random edge additions on cycle structures.
Key Takeaways
- •Investigates the number of random edges needed to create higher powers of Hamiltonian cycles.
- •Focuses on Pósa-Seymour graphs.
- •Determines thresholds, particularly 'over-thresholds'.
- •Provides bounds and specific results for different parameters.
- •Contributes to understanding graph properties and random edge effects.
Reference / Citation
View Original"The paper establishes asymptotically tight lower and upper bounds on the over-thresholds and shows that for infinitely many instances of m the two bounds coincide."