Reproduce “Optimal Mixing for Local Edge-Coloring Dynamics on Trees” on OpenResearch
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About this paper
Haoran wang
The authors prove local sampling of proper edge-colorings on finite trees with maximum degree Δ. Single-edge updates mix when q ≥ Δ + 2, while neighboring-edge updates mix when q ≥ Δ + 1. Prepared regions route displaced colors through the tree and return them, yielding worst-case total-variation mixing in OΔ(n(log n + log(1/ε))) updates. The n log n order is sharp for fixed Δ.
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