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Research notes on every problem, and a library of the papers behind them. Built from the open erdos repository.
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Lemmas
One row per claim, generated from claim _index.md frontmatter. Regenerate with erdos ledger; hand edits are overwritten.
| id | statement | area | status | tier | lean | link |
|---|---|---|---|---|---|---|
| L17 | For every integer k>=3, chi_S(n, floor(n^2/4)+1, C_{2k+1}) = n^2/8 + o(n^2) as n tends to infinity, where chi_S(n,e,G) is the least r for which some simple graph with n vertices and exactly e edges has an r-coloring of its edges under which every copy of G has pairwise distinct edge colors; a copy of C_{2k+1} is a cycle on 2k+1 distinct vertices of the graph. Equivalently chi_S(n, floor(n^2/4)+1, C_{2k+1}) / n^2 tends to 1/8. The value is taken as 0 for the finitely many n at which no graph on n vertices has floor(n^2/4)+1 edges; this does not affect the limit. | ramsey_theory | proved | 2 | Erdos.L17.claim | L17_rainbow_odd_cycle_threshold |
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