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Let be a graph with vertices such that every induced subgraph on vertices has more than edges. Must contain a triangle?
Source: erdosproblems.com/128
No claim settles this problem.
Falsifiable. The site's label is a note on an
open problem (Current assessment), not a claim; the site printed FALSIFIABLE
with the page last edited 31 October 2025. The frontmatter standing is derived
from the claim pages under claims/: four accepted partial claims prove the
statement on classes of graphs (Krivelevich; Keevash and Sudakov; Norin and
Yepremyan; Razborov; see Progress), and no claim addresses the general
question, so the problem stays open. Sarid's proof claim on the site's
proof-claims tab, the statement with replaced by
, settles no instance of the question as posed and
is recorded in the Current assessment, not as a claim; the site states that a
listing on the tab is no guarantee of correctness.