Open Research Index

Greedy Uniformity on Trees

John Fairfax-Ball

Palomar Registrypalomar/PALOMAR-2026-10-01-000003Oct 1, 2026math.COscore 0

Formalization of exact distributional results for the random-permutation greedy maximal-independent-set process on finite trees. For every finite nonempty tree, the complete greedy output law is uniform over maximal independent sets exactly for K1 and K2. For the mixed-spider family T_{k,l}, the development counts maximal independent sets, proves exact output probabilities, and for l=2^k-k proves positive total-variation bias with decay O(sqrt(k)/4^k), equivalently O(sqrt(log n_k)/n_k^2) along n_k=2^k+k+1. The Stage-4 novelty classification is "plausibly new with bounded uncertainty"; no…

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