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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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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

275 Problems

2/6

NumberQuestionOpen
#159No statement retained — open to read what the source holdsopenNo formal declaration
#163No statement retained — open to read what the source holdsprovedNo formal declaration
#165No statement retained — open to read what the source holdsopenNo formal declaration
#166No statement retained — open to read what the source holdsprovedNo formal declaration
#167No statement retained — open to read what the source holdsfalsifiableNo formal declaration
#180If F\mathcal{F} is a finite set of finite graphs then ex(n;F)\mathrm{ex}(n;\mathcal{F}) is the maximum number of edges a graph on nn vertices can have without containing any subgraphs from F\mathcal{F}. Note that it is trivial that ex(n;F)≤ex(n;G)\mathrm{ex}(n;\mathcal{F})\leq \mathrm{ex}(n;G) for every G∈FG\in\mathcal{F}. Is it true that, for every F\mathcal{F}, there exists G∈FG\in\mathcal{F} such that ex(n;G)≪Fex(n;F)?\mathrm{ex}(n;G)\ll_{\mathcal{F}}\mathrm{ex}(n;\mathcal{F})?open (Lean)Formalized
#181No statement retained — open to read what the source holdsopenNo formal declaration
#182No statement retained — open to read what the source holdsprovedNo formal declaration
#183Let R(3;k)R(3;k) be the minimal nn such that if the edges of KnK_n are coloured with kk colours then there must exist a monochromatic triangle. Determine lim⁡k→∞R(3;k)1/k.\lim_{k\to \infty}R(3;k)^{1/k}.open (Lean)Formalized
#184Any graph on nn vertices can be decomposed into O(n)O(n) many edge-disjoint cycles and edges.openFormalized
#426We say HH is a unique subgraph of GG if there is exactly one way to find HH as a subgraph (not necessarily induced) of GG. Is there a graph on nn vertices with ≫2(n2)n!\gg \frac{2^{\binom{n}{2}}}{n!} many distinct unique subgraphs?disproved (Lean)Formalized
#500No statement retained — open to read what the source holdsopenNo formal declaration
#518No statement retained — open to read what the source holdsprovedNo formal declaration
#533Let δ>0\delta > 0. If nn is sufficiently large and GG is a graph on nn vertices with no K5K_5 and at least δn2\delta n^2 edges, must GG contain a set of ≫δn\gg_\delta n vertices spanning no triangle?disprovedFormalized
#544No statement retained — open to read what the source holdsopenNo formal declaration
#545No statement retained — open to read what the source holdsopenNo formal declaration
#546No statement retained — open to read what the source holdsprovedNo formal declaration
#547No statement retained — open to read what the source holdsdecidableNo formal declaration
#548No statement retained — open to read what the source holdsfalsifiableNo formal declaration
#549No statement retained — open to read what the source holdsdisprovedNo formal declaration
#550No statement retained — open to read what the source holdsopenNo formal declaration
#551No statement retained — open to read what the source holdsdecidableNo formal declaration
#552No statement retained — open to read what the source holdsopenNo formal declaration
#553No statement retained — open to read what the source holdsprovedNo formal declaration
#554No statement retained — open to read what the source holdsopenNo formal declaration
#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
#571No statement retained — open to read what the source holdsopenNo formal declaration
#572No statement retained — open to read what the source holdsopenNo formal declaration
#573No statement retained — open to read what the source holdsopenNo formal declaration
#574No statement retained — open to read what the source holdsdisprovedNo formal declaration
#575No statement retained — open to read what the source holdsopenNo formal declaration
#576No statement retained — open to read what the source holdsopenNo formal declaration
#577No statement retained — open to read what the source holdsprovedNo formal declaration

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