Skip to content

Erdős Problems

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

Add a contributionCollection details
Collection coverage

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
More filters

Coverage is source-observation coverage, not Problem completeness. Inspect coverage

Problems

114 Problems

2/3

NumberQuestionOpen
#555No statement retained — open to read what the source holdsopenNo formal declaration
#556No statement retained — open to read what the source holdsdecidableNo formal declaration
#557No statement retained — open to read what the source holdsopenNo formal declaration
#558No statement retained — open to read what the source holdsopenNo formal declaration
#559No statement retained — open to read what the source holdsdisprovedNo formal declaration
#560No statement retained — open to read what the source holdsopenNo formal declaration
#561No 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
#565No statement retained — open to read what the source holdsprovedNo formal declaration
#566Let GG be such that any subgraph on kk vertices has at most 2k−32k-3 edges. Is it true that, if HH has mm edges and no isolated vertices, then r^(G,H)≪m\hat{r}(G,H) \ll m?openFormalized
#567Erdős Problem 567 (Q3)openFormalized
#568No statement retained — open to read what the source holdsopenNo formal declaration
#569No statement retained — open to read what the source holdsopenNo formal declaration
#570No statement retained — open to read what the source holdsprovedNo formal declaration
#582Does there exist a graph GG which contains no K4K_4, and yet any 22-colouring of the edges produces a monochromatic K3K_3?proved (Lean)Formalized
#590Let αα be the infinite ordinal ωω\omega^{\omega}. It was proved by Chang [Ch72] that any red/blue colouring of the edges of KαK_α there is either a red KαK_α or a blue K3K_3.provedFormalized
#591Let αα be the infinite ordinal ωω2\omega^{\omega^2}. Is it true that any red/blue colouring of the edges of KαK_α there is either a red KαK_α or a blue K3K_3?provedFormalized
#592Determine which countable ordinals ββ have the property that, if α=ωβα = \omega^β, then in any red/blue colouring of the edges of KαK_α there is either a red KαK_α or a blue K3K_3.openFormalized
#596Erdős Problem 596 (Erdős–Hajnal, [Er87]). For which graph pairs (G1,G2)(G_1, G_2) is it true thatopenFormalized
#597No statement retained — open to read what the source holdsopenNo formal declaration
#598Erdős Problem 598: Let mm be an infinite cardinal and κ\kappa be the successor cardinal of 2ℵ02^{\aleph_0}. Can one colour the countable subsets of mm using κ\kappa many colours so that every X⊆mX \subseteq m with ∣X∣=κ|X| = \kappa contains subsets of all possible colours?openFormalized
#609No statement retained — open to read what the source holdsopenNo formal declaration
#615Does there exist some constant c>0c > 0 such that for all sufficiently large nn, if GG is a graph with nn vertices and at least (1/8−c)n2(1/8 - c)n^2 edges then GG must contain either a K4K_4 or an independent set on at least n/log⁡nn/\log n vertices?disprovedFormalized
#636No statement retained — open to read what the source holdsprovedNo formal declaration
#637No statement retained — open to read what the source holdsprovedNo formal declaration
#638No statement retained — open to read what the source holdsopenNo formal declaration
#639Is it true that if the edges of KnK_n are 2-coloured then there are at most n2/4n^2/4 many edges which do not occur in a monochromatic triangle?proved (Lean)Formalized
#645If ℕ is 22-coloured then there must exist a monochromatic three-term arithmetic progression x,x+d,x+2dx,x+d,x+2d such that d>xd>x.proved (Lean)Formalized
#667No statement retained — open to read what the source holdsopenNo formal declaration
#720No statement retained — open to read what the source holdsprovedNo formal declaration
#721No statement retained — open to read what the source holdssolvedNo formal declaration
#800No statement retained — open to read what the source holdsprovedNo formal declaration
#801No statement retained — open to read what the source holdsprovedNo formal declaration
#809No statement retained — open to read what the source holdsopenNo formal declaration
#810No statement retained — open to read what the source holdsopenNo formal declaration
#811No statement retained — open to read what the source holdsopenNo formal declaration
#812Is it true that R(n+1)R(n)≥1+c\frac{R(n+1)}{R(n)}\geq 1+c for some constant c>0c>0, for all large nn?openFormalized
#894No statement retained — open to read what the source holdsprovedNo formal declaration
#911No statement retained — open to read what the source holdsopenNo formal declaration
#924No statement retained — open to read what the source holdsprovedNo formal declaration
#925No statement retained — open to read what the source holdsdisprovedNo formal declaration
#948No statement retained — open to read what the source holdssolvedNo formal declaration
#949Let S⊆RS \subseteq \mathbb{R} be a set containing no solutions to a+b=ca + b = c. Must there be a set A⊆R∖SA \subseteq \mathbb{R} \setminus S of cardinality continuum such that A+A⊆R∖SA + A \subseteq \mathbb{R}\setminus S?openFormalized
#965Erdős asks in [Er75b] if for every 2-coloring of ℝ, there is an uncountable set A⊆RA ⊆ ℝ such that all sums a+ba + b for a,b∈A,a≠ba, b ∈ A, a ≠ b have the same colour.disprovedFormalized
#966Let k,r≥2k,r\geq 2. Does there exist a set A⊆NA\subseteq \mathbb{N} that contains no non-trivial arithmetic progression of length k+1k+1, yet in any rr-colouring of AA there must exist a monochromatic non-trivial arithmetic progression of length kk?proved (Lean)Formalized
#986No statement retained — open to read what the source holdsprovedNo formal declaration

Search problems.science

Find a Problem, Result, source, or page