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Erdős Problems

1,217 source-owned questions · 604 with a formal statement · searchable by statement, number, topic and source status.

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Collection coverage

Source status, exact formal material, and reviewed Results are separate signals.

  • Open per source608
  • Resolved per source556
  • Other source status53
Exact formal statement available604 / 1,217
With Repository-reviewed evidence2 / 1,217
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Problems

31 Problems

NumberQuestionOpen
#207No statement retained — open to read what the source holdsprovedNo formal declaration
#500No statement retained — open to read what the source holdsopenNo formal declaration
#562Let Rr(n)R_r(n) denote the rr-uniform hypergraph Ramsey number: the minimal mm such that if we 22-colour all edges of the complete rr-uniform hypergraph on mm vertices then there must be some monochromatic copy of the complete rr-uniform hypergraph on nn vertices.openFormalized
#563No statement retained — open to read what the source holdsopenNo formal declaration
#564Let R3(n)R_3(n) be the minimal mm such that if the edges of the 33-uniform hypergraph on mm vertices are 22-coloured then there is a monochromatic copy of the complete 33-uniform hypergraph on nn vertices.openFormalized
#593Erdős Problem 593 (500): Characterize those finite 3-uniform hypergraphs which appear in every 3-uniform hypergraph of chromatic number >ℵ0> \aleph_0.openFormalized
#643No statement retained — open to read what the source holdsopenNo formal declaration
#712No statement retained — open to read what the source holdsopenNo formal declaration
#716No statement retained — open to read what the source holdsproved (Lean)No formal declaration
#719No statement retained — open to read what the source holdsopenNo formal declaration
#747No statement retained — open to read what the source holdssolvedNo formal declaration
#775Is there a 33-uniform hypergraph on nn vertices which contains at least n−O(1)n-O(1) different sizes of cliques (maximal complete subgraphs)?disproved (Lean)Formalized
#780No statement retained — open to read what the source holdsprovedNo formal declaration
#794Is it true that every 33-uniform hypergraph on 3n3n vertices with at least n3+1n^3+1 edges must contain either a subgraph on 44 vertices with 33 edges or a subgraph on 55 vertices with 77 edges?disproved (Lean)Formalized
#832No statement retained — open to read what the source holdsdisprovedNo formal declaration
#833No statement retained — open to read what the source holdsprovedNo formal declaration
#834No statement retained — open to read what the source holdssolvedNo formal declaration
#835It is known that for 3≤k≤83 \leq k \leq 8, the chromatic number of J(2k,k)J(2k, k) is greater than k+1k+1, see [Johnson graphs](https://aeb.win.tue.nl/graphs/Johnson.html).verifiableFormalized
#836No statement retained — open to read what the source holdsopenNo formal declaration
#837No statement retained — open to read what the source holdsopenNo formal declaration
#901No statement retained — open to read what the source holdsopenNo formal declaration
#1020No statement retained — open to read what the source holdsfalsifiableNo formal declaration
#1022Is there a constant ctc_t, where ct→∞c_t\to \infty as t→∞t\to \infty, such that if F\mathcal{F} is a finite family of finite sets, all of size at least tt, and for every set XX there are <ct∣X∣<c_t\lvert X\rvert many A∈FA\in \mathcal{F} with A⊆XA\subseteq X, then F\mathcal{F} has chromatic number 22 (in other words, has property B)?proved (Lean)Formalized
#1024No statement retained — open to read what the source holdssolvedNo formal declaration
#1075No statement retained — open to read what the source holdsopenNo formal declaration
#1076No statement retained — open to read what the source holdsprovedNo formal declaration
#1128Erdős Problem 1128 (disproved by Prikry–Mills, 1978):disprovedFormalized
#1157No statement retained — open to read what the source holdsopenNo formal declaration
#1158No statement retained — open to read what the source holdsopenNo formal declaration
#1177No statement retained — open to read what the source holdsopenNo formal declaration
#1178No statement retained — open to read what the source holdsopenNo formal declaration

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