Research notes on every problem, and a library of the papers behind them. Built from the open erdos repository.
Updated
Claim. The answer to Problem 1010 is yes, the same statement that Lovász and Simonovits prove. The site credits V. S. Nikiforov and N. G. Khadzhiivanov, Solution of the problem of P. Erdős on the number of triangles in graphs with vertices and edges, C. R. Acad. Bulgare Sci. 34 (1981), 969--970, with an independent proof. The page's date is the note's year; the day is not recorded in any source read.
Depends on. Nothing in this wiki; the result is known only through the site's citation.
Acceptance. The reviewed evidence is documented acceptance by the
site's curator, Thomas Bloom, who labels the problem PROVED and names this
note as one of its two independent proofs, with the community database in
agreement (it lists the problem as proved as of its last update, 10
September 2025). Nothing else is in hand. The
note is not held: a Crossref bibliographic query returned
nothing relevant and no other online record was found; no text has been
read, and no referee record is known, so refereed is not listed. A 1988
single-author paper of Khadzhiivanov on the common-edge triangle problem of
Problem 905, once associated
with this problem, is not this note.
Reopening condition: a copy of the note, after which its statement is paged
and compared with the site's. The problem's standing also rests on the
Lovász--Simonovits page, whose 1983 text has been read (no file is held).