Observed arrival · 2026-09-17
Graceful Tree Search: Can Every Tree Be Labelled?
A distributed-computing project investigates a mathematical conjecture that every tree can receive a graceful labelling.
Field notes
Graceful Tree Search divides an exhaustive finite search into blocks that can run on volunteered computers. The page describes a 36-dot search containing 524,288 blocks and reports 765 validated blocks with 129 still in flight. Its mathematical test assigns the numbers 0 through n−1 to a tree’s dots and checks whether the resulting line differences use every value from 1 through n−1 exactly once. Earlier searches are reported to cover all trees up to 35 dots.
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