Every problem here was open when it entered the pool.
Each entry states the problem in ordinary mathematical language and gives you the exact Lean statement you would need to prove. Nothing is paraphrased, so what you read is what gets checked.
Combinatorics
Erdős problem 579
Let δ>0. If n is sufficiently large and G is a graph on n vertices with no
K2,2,2
(the octahedron) and at least
δn2
edges, must
G
contain an independent
set of size
≫δn
?
This is a problem of Erdős, Hajnal, Sós, and Szemerédi [EHSS83]. It is **open**; they proved
the statement for
δ>1/8
(see
erdos_579.variants.ehss_large_delta
), and the
difficulty is to push the edge-density threshold down to an arbitrary
δ>0
.
Here
K2,2,2
is the complete tripartite graph with all parts of size
2
, encoded as
completeMultipartiteGraph (fun _ : Fin 3 => Fin 2)
A statement that does not faithfully capture the original conjecture is the one real risk here, so we would rather hear about it early - before someone spends weeks on it.