PPL 035 / 177 permanent IDsPrize Problem Ledger · PPLChecked 2026.07.26
Prize Problem LedgerErdősPPL 035Erdős Problem #1029

Permanent problem IDPPL 035

Verified openErdősconjecture

Graph theory

Erdős Problem #1029

If R(k) is the Ramsey number for K_k, the minimal n such that every 2-colouring of the edges of K_n contains a monochromatic copy of K_k, then \frac{R(k)}{k2^(k/2)}→ ∈fty.

graph theoryramsey theory
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The problem

If R(k) is the Ramsey number for K_k, the minimal n such that every 2-colouring of the edges of K_n contains a monochromatic copy of K_k, then \frac{R(k)}{k2^(k/2)}→ ∈fty.

Open since1935source estimate
Last checked2026.07.26Catalog verification
02

Reward offers

Offer 01$100Paul Erdős / Combinatorics Foundation
Documented

A solution must appear in a reputable journal, with documentation that Erdős offered the displayed amount. Claims are administered by the Combinatorics Foundation; erdosproblems.com does not pay awards.

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Sources & reading