Exact Rainbow Numbers for Cycle-Related Graphs in Multi-Hubbed Wheels

Research Paper #Graph Theory, Combinatorics 🔬 Research|Analyzed: Jan 3, 2026 19:33•

Published: Dec 28, 2025 06:55

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1 min read

Analysis

This paper determines the exact rainbow number for specific graph structures (multi-hubbed wheels and chorded cycles) which is important for applications in areas like wireless communication and network analysis. It solves problems proposed by previous researchers and generalizes existing results, providing a complete solution for rainbow numbers of cycles in large wheel graphs.

Key Takeaways

•Provides exact formulas for rainbow numbers in multi-hubbed wheel graphs.
•Solves open problems from previous research.
•Generalizes existing results on rainbow numbers in wheel graphs.
•The results are applicable to diverse fields like wireless communication and network analysis.

Reference / Citation

View Original

"The paper determines the exact rainbow number rb(G, H) where G is a multi-hubbed wheel graph W_d(s) and H = θ_{t,ℓ} represents a cycle C_t of length t with 0 ≤ ℓ ≤ t-3 chords emanating from a common vertex."

ArXivDec 28, 2025 06:55

* Cited for critical analysis under Article 32.

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