Skip to content

Erdős problem 183

Start work

Let R(3;k)R(3;k) be the least nn such that every kk-colouring of the edges of KnK_n contains a monochromatic triangle. Determine lim⁡k→∞R(3;k)1/k\lim_{k\to\infty} R(3;k)^{1/k} (a $250 Erdős prize problem). A superexponential lower bound resolves the problem: the limit is infinite.

How the state got here

0 of 6 recorded
  1. Prior stateNone retained
  2. WorkNo submitted work retained
  3. VerificationNo check retained
  4. DecisionNo Repository has decided
  5. StandingNothing recorded here
  6. Next gapNot recorded

Result history

Published changes, performers, checks, and later corrections.

No result history yet
No proposed change is retained for this Problem, so there is nothing to show a decision on.

Correction history

No correction history

Technical detailsExact roots, source, and retained record identifiers

Exact provenance

Problem row
sha256:138ff3a6271bd79f10f2433bb9a1f755b6833ba61e8b03c733984a18479e6d84
Metadata
sha256:a0efc989c88cec9ab1bcff1535641e0db7809bccb1914b7950ef12014cb254c7
Observation
sha256:9c8326e865b6017b103af7611c852a06776d81964979b8ab5a1b800cd550dff6
Content
sha256:0552d039738a4b2f0b393abb13a43cacbb14667cd1ce090f05112b003684e593
Repository
sha256:a956b84c437202e5a02cc9e036a621bd14a302b34a75758115730bdbb77c52a4
Projection
sha256:a4a96441668a9f8b33afbcb3f696a2639f5fae145f36ddc063d7f67d5fb87ce8
Source commit
36c6d0fef71a3fec84d9dcd5eeca4e22e378f7cb
Upstream sourceInspect recordsSource JSON