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declared open · $500erdos:500
Erdős problem 500
graph theoryhypergraphsturan numberA140462
declared open · formalizederdos:562
True ↔ ∀ r ≥ 3, (fun n => Real.log^[r - 1] ↑(Combinatorics.hypergraphRamsey r n)) =Θ[Filter.atTop] fun n => ↑n
graph theoryramsey theoryhypergraphspossible2 sources
declared openerdos:563
Erdős problem 563
graph theoryramsey theoryhypergraphsN/A
declared open · formalized · $500erdos:564
True ↔ ∃ c > 0, ∀ᶠ (n : ℕ) in Filter.atTop, 2 ^ 2 ^ (c * n) ≤ ↑(Combinatorics.hypergraphRamsey 3 n)
graph theoryramsey theoryhypergraphspossible2 sources
declared open · formalized · $500erdos:593
Which finite triple systems occur in every triple system of uncountable chromatic number? The claimed characterization: exactly those that, after removing isolated vertices, are linear, have every hyperedge-node of their Levi graph meeting a bridge, and have every Berge cycle even.
set theorygraph theoryhypergraphsN/A4 sources
declared openerdos:643
Erdős problem 643
graph theoryhypergraphspossible
declared open · $500erdos:712
Erdős problem 712
graph theoryturan numberhypergraphspossible
declared openerdos:719
Erdős problem 719
graph theoryhypergraphspossible
declared openerdos:836
Erdős problem 836
graph theoryhypergraphschromatic numberN/A2 sources
declared openerdos:837
Erdős problem 837
graph theoryhypergraphsN/A
declared openerdos:901
Erdős problem 901
combinatoricshypergraphspossible
declared openerdos:1075
Erdős problem 1075
hypergraphsN/A
declared openerdos:1157
Erdős problem 1157
hypergraphsturan numberpossible
declared openerdos:1158
Erdős problem 1158
hypergraphsturan numberpossible
declared openerdos:1177
For a finite forbidden triple system GG, what exact uncountable chromatic cardinalities occur among GG-free triple systems, and how do those spectra interact? The revised manuscript answers the three exact-cardinal questions and claims a complete spectrum dichotomy.
set theorychromatic numberhypergraphsN/A3 sources
declared openerdos:1178
Erdős problem 1178
graph theoryhypergraphsN/A

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