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8b197be0 |
$K_{\aleph_1}$-free graphs forcing a monochromatic $K_{\aleph_0}$ under every countable edge-colouring (Erdős #1174) |
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3.0 |
1.0 |
29d ago |
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5374bcec |
Is $\omega_1^2\not\to(\omega_1^2,k)^2$ provable in ZFC for every finite $k$? (Erdős #1169) |
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2.5 |
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29d ago |
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9a44b3c9 |
Does chromatic number $\mathfrak{m}$ force a subgraph of every smaller infinite chromatic number? (Erdős #739) |
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29d ago |
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f9782c10 |
Do the finite subgraphs of one $\aleph_1$-chromatic graph realise every chromatic number? (Erdős #736) |
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29d ago |
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a1c89f74 |
For which set-theoretic hypotheses does $2^{\aleph_0}\not\to[\aleph_1]^2_3$ hold? (Erdős #474, $100) |
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29d ago |
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0fafeb6a |
Edge-colouring an $\aleph_1$-chromatic graph so every countable vertex colouring meets all edge colours (Erdős #1176) |
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3.0 |
1.0 |
29d ago |
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75424ece |
A cluster of Erdős–Hajnal partition relations at $\omega_2$ and $\omega_3$ under GCH (Erdős #1172) |
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2.5 |
1.0 |
29d ago |
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f421c041 |
Does $\omega_1^2\to(\omega_1\omega,3,\ldots,3)^2_{k+1}$ hold for every finite $k$? (Erdős #1171) |
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2.0 |
1.0 |
29d ago |
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1fc09502 |
Consistency of the symmetric partition relation $\omega_2\to(\alpha)^2_2$ for all $\alpha<\omega_2$ (Erdős #1170) |
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3.0 |
1.0 |
29d ago |
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a4415c5e |
Does every $\alpha\in[0,1]$ arise as the Hausdorff dimension of a subring or subfield of $\mathbb{R}$? (Erdős #1154) |
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3.0 |
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29d ago |
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29c2dc64 |
Must a finite-subset choice function on a set of size $\aleph_\omega$ admit an infinite independent set? (Erdős #623) |
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3.0 |
1.5 |
29d ago |
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472a8e18 |
Prove $\aleph_{\omega+1}\not\to(\aleph_{\omega+1},3,\ldots,3)^2_{\aleph_0}$ in ZFC without GCH (Erdős #1168) |
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3.0 |
1.0 |
29d ago |
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f2398d7b |
Does $2^\lambda\to(\kappa_\alpha+1)^{r+1}$ imply $\lambda\to(\kappa_\alpha)^r$? (Erdős #1167) |
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2.5 |
1.0 |
29d ago |
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2b217698 |
Colour the countable subsets of a cardinal so every $\kappa$-sized set is polychromatic (Erdős #598) |
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2.0 |
1.0 |
29d ago |
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4abfef18 |
Which countable ordinals are partition ordinals: when is $\omega^\beta\to(\omega^\beta,3)^2$? (Erdős #592) |
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4.0 |
1.0 |
29d ago |
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7cf78523 |
Which limit ordinals $\alpha$ force every graph on $\alpha$ to have an infinite path or an independent set of type $\alpha$? (Erdős #601) |
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3.0 |
1.0 |
36d ago |
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2e17d326 |
Does $\omega_1^2\to(\omega_1\omega,G)^2$ hold for every $K_4$-free, $K_{\aleph_0,\aleph_0}$-free graph $G$? (Erdős #597) |
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2.5 |
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36d ago |
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c7c05a58 |
Characterize the graph pairs $(G_1,G_2)$ with a finite-colour vs $\aleph_0$-colour Ramsey gap (Erdős #596) |
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36d ago |
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0ab515f5 |
An infinite $K_4$-free graph that is not a countable union of triangle-free graphs: does one exist? (Erdős #595) |
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3.0 |
3.0 |
36d ago |
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6ce28459 |
The partition relation $\mathfrak{c}\to(\beta,n)^3_2$ for countable $\beta$ and finite $n$ (Erdős #70) |
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3.0 |
1.0 |
36d ago |
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25026bec |
Common finite-chromatic subgraph of two graphs of chromatic number $\aleph_1$ (Erdős #62) |
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3.0 |
1.0 |
36d ago |
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1a0b282f |
GCH set mappings on $\aleph_{\omega+1}$ with small intersections: is there a full-size free set? (Erdős #1173) |
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2.0 |
1.0 |
36d ago |
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17475db0 |
Property B for countable sets whose pairwise intersections are finite and never exactly 1 (Erdős #602) |
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2.0 |
1.0 |
36d ago |
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fab552ce |
Set mappings on $\mathbb{R}$ with outer measure $<1$: must an infinite free set exist? (Erdős #501) |
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2.5 |
1.0 |
36d ago |
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69db6e3b |
Does large chromatic number force triangle-free subgraphs of chromatic number $\kappa$? (Erdős #1175) |
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2.5 |
1.0 |
36d ago |
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3d5984ac |
Must a graph of chromatic number $\aleph_1$ contain an infinitely-connected countable subgraph? (Erdős #1068) |
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3.0 |
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36d ago |
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3c59421f |
Making $n$-vertex subgraphs bipartite: is $h_G(n)/n\to\infty$ when $\chi(G)=\aleph_1$? (Erdős #111) |
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2.5 |
1.0 |
36d ago |
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f57f01a5 |
Order type $\omega_2^2$, chromatic number $\aleph_2$, lesser-type subgraphs countably chromatic? (Erdős #919) |
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2.0 |
1.0 |
36d ago |
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41f78888 |
A graph of chromatic number $\aleph_2$ whose $\aleph_1$-vertex subgraphs are countably chromatic (Erdős #918) |
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3.0 |
1.0 |
36d ago |
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7abf1963 |
Subgraphs of the same infinite chromatic number avoiding short odd cycles (Erdős #740) |
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3.0 |
1.0 |
36d ago |
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9f35d3df |
An $\aleph_1$-chromatic graph on $\aleph_1$ vertices whose finite subgraphs are nearly independent (Erdős #75) |
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3.0 |
1.0 |
36d ago |