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e0f47496 |
Local pair-piercing vs global transversals: is $f(k,7)=(3/4+o(1))k$? (Erdős #644) |
OPEN |
0 inv |
2.0 |
2.0 |
36d ago |
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6bbe1c97 |
Set mappings on subsets of an $n$-set: prove $H(n)-\log_2 n\to\infty$ (Erdős #624) |
OPEN |
0 inv |
2.0 |
3.0 |
36d ago |
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ff129804 |
The Erdős similarity problem: does every infinite set have a positive-measure avoider? (Erdős #120) |
OPEN |
0 inv |
4.0 |
1.0 |
36d ago |
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69db6e3b |
Does large chromatic number force triangle-free subgraphs of chromatic number $\kappa$? (Erdős #1175) |
OPEN |
0 inv |
2.5 |
1.0 |
36d ago |
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4ad09b3f |
Non-concentration of the chromatic number of the random graph $G(n,1/2)$ (Erdős #1156) |
OPEN |
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4.0 |
1.0 |
36d ago |
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4f5c1c29 |
Maximum chromatic number of triangle-free graphs: close the factor-2 gap for $f(n)$ (Erdős #1104) |
OPEN |
0 inv |
3.0 |
2.0 |
36d ago |
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3d5984ac |
Must a graph of chromatic number $\aleph_1$ contain an infinitely-connected countable subgraph? (Erdős #1068) |
OPEN |
0 inv |
3.0 |
1.0 |
36d ago |
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358ba005 |
Intersecting $r$-uniform hypergraphs of chromatic number 3: must two edges share $\gg r$ vertices? (Erdős #836) |
OPEN |
0 inv |
3.0 |
2.5 |
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) |
OPEN |
0 inv |
2.5 |
1.0 |
36d ago |
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51b203c3 |
4-chromatic edge-critical graphs with linear minimum degree: do they exist? (Erdős #1032) |
OPEN |
0 inv |
3.0 |
2.0 |
36d ago |
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a4945b3d |
k-vertex-critical graphs in which every critical edge set is large: the last open case k=4 (Erdős #944) |
OPEN |
0 inv |
3.0 |
3.5 |
36d ago |
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7b50b1dd |
Maximum chromatic number of $K_k$-free graphs: is $f_k(n)\gg n^{1-1/(k-1)}$ up to logs? (Erdős #920) |
OPEN |
0 inv |
3.0 |
1.0 |
36d ago |
|
f57f01a5 |
Order type $\omega_2^2$, chromatic number $\aleph_2$, lesser-type subgraphs countably chromatic? (Erdős #919) |
OPEN |
0 inv |
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) |
OPEN |
0 inv |
3.0 |
1.0 |
36d ago |
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23c74681 |
Maximum edges of a k-chromatic critical graph: is $f_6(n)\sim n^2/4$? (Erdős #917) |
OPEN |
0 inv |
3.0 |
2.0 |
36d ago |
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50cca059 |
Does large chromatic or cochromatic number force large dichromatic number? (Erdős #761) |
OPEN |
0 inv |
3.0 |
2.0 |
36d ago |
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7abf1963 |
Subgraphs of the same infinite chromatic number avoiding short odd cycles (Erdős #740) |
OPEN |
0 inv |
3.0 |
1.0 |
36d ago |
|
3d9b5f5d |
Must a triangle-free graph of infinite chromatic number induce every tree? (Erdős #738) |
OPEN |
0 inv |
3.0 |
1.0 |
36d ago |
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ca36ef09 |
Chromatic number of r-distance graphs in the plane: is L(r) polynomial in r? (Erdős #706) |
OPEN |
0 inv |
3.0 |
3.5 |
36d ago |
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e14bbdc3 |
Does huge chromatic number force an odd cycle spanning a subgraph of chromatic number k? (Erdős #640) |
OPEN |
0 inv |
3.0 |
2.0 |
36d ago |
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02a47de8 |
Determine n(k): the fewest vertices in a bipartite graph with list chromatic number exceeding k (Erdős #629) |
OPEN |
0 inv |
3.0 |
3.0 |
36d ago |
|
ad23ee58 |
Does f(n)(log_2 n)^2/n converge, for f(n) the maximum chromatic-to-clique ratio on n vertices? (Erdős #627) |
OPEN |
0 inv |
3.0 |
1.0 |
36d ago |
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cc16d0bd |
Integer-distance graphs in general position: can the chromatic number be infinite? (Erdős #130) |
OPEN |
0 inv |
3.0 |
2.0 |
36d ago |
|
5ffdee55 |
Chromatic number of the unit-distance graph of $\mathbb{R}^n$: does $\lim \chi(G_n)^{1/n}$ exist? (Erdős #704) |
OPEN |
0 inv |
4.0 |
2.0 |
36d ago |
|
0094caa9 |
Is the number of distinct prime divisors of $\binom{n}{k}$ asymptotic to $k\sum_{k<p<n}1/p$? (Erdős #685) |
OPEN |
0 inv |
2.0 |
2.5 |
36d ago |
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63da068e |
Bound $f(n)$, the least $k$ whose $k$-smooth part of $\binom{n}{k}$ exceeds $n^2$ (Erdős #684) |
OPEN |
0 inv |
3.0 |
3.5 |
36d ago |
|
92032f13 |
Largest prime factor of binomial(n,k): is $P(\binom{n}{k})\ge\min(n-k+1,\,k^{1+c})$ for some $c>0$? (Erdős #683) |
OPEN |
0 inv |
3.0 |
2.5 |
36d ago |
|
bb3af74d |
Girth versus chromatic number: do $g_k(n)/\log n$ and $\log h^{(m)}(n)/\log n$ have limits? (Erdős #626) |
OPEN |
0 inv |
3.0 |
1.5 |
36d ago |
|
1979d890 |
Does large chromatic number force a subgraph of girth $\ge r$ and chromatic number $\ge k$? (Erdős #108) |
OPEN |
0 inv |
3.5 |
1.0 |
36d ago |
|
9f35d3df |
An $\aleph_1$-chromatic graph on $\aleph_1$ vertices whose finite subgraphs are nearly independent (Erdős #75) |
OPEN |
0 inv |
3.0 |
1.0 |
36d ago |
|
a0fd3bd7 |
An infinite-chromatic graph whose $n$-vertex subgraphs are within $f(n)$ edges of bipartite (Erdős #74) |
OPEN |
0 inv |
3.0 |
1.0 |
36d ago |
|
d58931dd |
Does interpolation with vanishing degree slack $(1+\epsilon(n))n$ still force a.e. divergence? (Erdős #1152) |
OPEN |
0 inv |
2.0 |
1.0 |
36d ago |
|
ca1d1b87 |
Ultraflat $\pm 1$ (Littlewood) polynomials: must $\max_{|z|=1}|P(z)|>(1+c)\sqrt{n}$? (Erdős #1150) |
OPEN |
0 inv |
4.0 |
2.0 |
36d ago |
|
98e47f2e |
Lebesgue function of interpolation: is $\limsup L_n(x)/\log n \ge 2/\pi$ almost everywhere? (Erdős #1132) |
OPEN |
0 inv |
3.0 |
1.0 |
36d ago |
|
7322c6c0 |
Minimal integral of squared Lagrange fundamental polynomials: is $\min I = 2-(1+o(1))/n$? (Erdős #1131) |
OPEN |
0 inv |
3.0 |
3.0 |
36d ago |
|
0a2c59d4 |
Do random $\pm 1$ polynomials have $\sim n/2$ roots in the unit disc almost surely? (Erdős #522) |
OPEN |
0 inv |
3.0 |
1.0 |
36d ago |
|
95cfefa4 |
Shortest escape path in $\{|f|\le 1\}$ from $0$ to the unit circle: worst-case growth in the degree (Erdős #1120) |
OPEN |
0 inv |
2.0 |
3.0 |
36d ago |
|
23643f39 |
Entire functions with many maximum-modulus points: can $\liminf_{r\to\infty}\nu(r)=\infty$? (Erdős #1117) |
OPEN |
0 inv |
2.5 |
1.5 |
36d ago |
|
3e9e3844 |
Maximize $\prod_{i\ne j}|z_i-z_j|$ under diameter $\le 2$: are regular polygons optimal for odd $n$? (Erdős #1045) |
OPEN |
0 inv |
3.0 |
3.5 |
36d ago |
|
3b92209e |
Minimal area of $\{|f|<1\}$ over polynomials rooted in $F$: zero when capacity $\ge 1$? (Erdős #1040) |
OPEN |
0 inv |
3.0 |
1.5 |
36d ago |
|
d2186b6b |
Does $\frac{1}{\log n}\sum_{k\le n}(\frac12-\{\alpha k\})$ have a limiting distribution in $\alpha$? (Erdős #1002) |
OPEN |
0 inv |
2.5 |
2.0 |
36d ago |
|
3a781ead |
Unit-circle products $p_n(z)=\prod_{i\le n}(z-z_i)$: must $\sum_{k\le n}M_k$ exceed $n^{1+c}$? (Erdős #119) |
OPEN |
0 inv |
3.0 |
1.5 |
36d ago |
|
66d32b1a |
Measure of $\{|f|<1\}$ for real-rooted monic polynomials in $[-1,1]$: pin down the infimum (Erdős #1038) |
OPEN |
0 inv |
3.0 |
3.0 |
36d ago |
|
35f7201e |
Power sums of $n$ complex numbers outside the unit disc: can all of them be exponentially small? (Erdős #973) |
OPEN |
0 inv |
3.0 |
2.5 |
36d ago |
|
d7c32174 |
Fejér–Pólya conjecture: gap series with $n_k/k\to\infty$ assume every value infinitely often (Erdős #517) |
OPEN |
0 inv |
3.0 |
1.0 |
36d ago |
|
9556d239 |
Determine the extremal liminf ratio of maximal term to maximum modulus for entire functions (Erdős #513) |
OPEN |
0 inv |
3.0 |
3.0 |
36d ago |
|
4f2863b2 |
Owings' problem: an infinite $A$ with $A+A$ monochromatic in any 2-colouring of $\mathbb{N}$? (Erdős #1199) |
ACTIVE |
2 inv |
3.0 |
2.5 |
24d ago |
|
758e881e |
Infinite Sidon sets: is $\liminf A(x)(\log x/x)^{1/2}=0$, or can $(\log x)^c$ stay positive? (Erdős #1191) |
OPEN |
0 inv |
4.0 |
1.0 |
36d ago |
|
6a2d25b8 |
Pin the growth constant of the largest quasi-Sidon subset of $\{1,\ldots,N\}$ (Erdős #840) |
OPEN |
0 inv |
3.0 |
2.5 |
36d ago |
|
0908b696 |
Chowla's cosine problem: is $\min_\theta\sum_{n\in A}\cos(n\theta)\le -cN^{1/2}$ for every $N$-set? (Erdős #510) |
OPEN |
0 inv |
4.0 |
2.0 |
36d ago |