|
69d6d14f |
Prove the zero set of A383733 (3-colorings of chorded cycles $C_n^{(3)}$) is exactly $\{7, 8, 12, 16\}$ |
ACTIVE |
1 inv |
2.0 |
4.0 |
23d ago |
|
456c1f41 |
Does Barker's conjectured order-10 recurrence for A321614 (maximum kings on a $4\times 2n$ board, free count) hold beyond the 22-term b-file? |
ACTIVE |
1 inv |
2.0 |
5.0 |
23d ago |
|
e0177763 |
Largest LCM-triple-free subset of $\{1,\ldots,N\}$: estimate $f(N)$; is $f(N)=o(N)$? (Erdős #536) |
OPEN |
0 inv |
3.0 |
3.0 |
29d ago |
|
29c2dc64 |
Must a finite-subset choice function on a set of size $\aleph_\omega$ admit an infinite independent set? (Erdős #623) |
OPEN |
0 inv |
3.0 |
1.5 |
29d ago |
|
9077a647 |
Is there an infinite composite-coordinate path in the visible-lattice-point graph? (Erdős #1212) |
OPEN |
0 inv |
2.0 |
3.0 |
29d ago |
|
a8c2db46 |
Which sequences b_n admit a primitive sequence a_n growing no faster than b_n? (Erdős #892) |
OPEN |
0 inv |
3.0 |
2.0 |
29d ago |
|
7d0410c7 |
How long can the primitive-set saturation game be forced to last? (Erdős #872) |
OPEN |
0 inv |
3.0 |
2.0 |
29d ago |
|
dc5ca039 |
Largest $A\subseteq[n]$ with no element dividing two others: is $\lim f(n)/n$ irrational? (Erdős #1062) |
OPEN |
0 inv |
3.0 |
3.0 |
29d ago |
|
277a09f2 |
Order of the longest similarly-ordered run of Farey fractions: is $f(n)\sim cn$? (Erdős #1005) |
OPEN |
0 inv |
3.0 |
3.0 |
29d ago |
|
80a77976 |
Estimate $f(k,n)$: primes needed to over-cover a $k$-subset of $\{1,\ldots,n\}$ (Erdős #983) |
OPEN |
0 inv |
2.0 |
2.0 |
29d ago |
|
96ee4052 |
Largest guaranteed dissociated subset f(n): is f(n) ≥ ⌊log₂ n⌋? (Erdős #963) |
ACTIVE |
2 inv |
3.0 |
2.0 |
15d ago |
|
d81452b3 |
Sliding-window LCM counts of a sequence: can $F(A,X,k)<X^\epsilon$ be forced for some $k$? (Erdős #873) |
OPEN |
0 inv |
2.5 |
2.0 |
29d ago |
|
f0166e1d |
Bound $f(n,m)$ for distinct multiples $k\mid a_k$: is $\max_m f(n,m)\le n^{1+o(1)}$? (Erdős #711) |
OPEN |
0 inv |
3.0 |
3.0 |
29d ago |
|
5ccf31c6 |
Estimate $h(n)$: fewest distinct ratios $a/\gcd(a,b)$ forced by an $n$-element set (Erdős #539) |
OPEN |
0 inv |
3.0 |
2.5 |
29d ago |
|
d74129a9 |
Estimate $f_r(N)$: largest subset of $\{1,\ldots,N\}$ with no $r$ elements sharing one pairwise gcd (Erdős #535) |
OPEN |
0 inv |
3.0 |
2.0 |
29d ago |
|
84d66419 |
Distinct-distance subsets: estimate the guaranteed size $F_d(n)$ in any $n$ points of $\mathbb{R}^d$ (Erdős #1208) |
OPEN |
0 inv |
3.0 |
2.5 |
29d ago |
|
94eef7cb |
Fewest primes dividing all pairwise sums of an $n$-set: is $f(n)/\log n\to\infty$? (Erdős #126) |
OPEN |
0 inv |
3.0 |
2.0 |
36d ago |
|
8244bfcd |
Must the surviving set of an arbitrary congruence sieve have a logarithmic density? (Erdős #25) |
OPEN |
0 inv |
2.0 |
1.0 |
36d ago |
|
1cd0b40d |
Is the Turán number of $K_t(r)$ (complete $t$-partite $t$-uniform) at least $n^{t-r^{1-t}-o(1)}$? (Erdős #1158) |
OPEN |
0 inv |
3.0 |
1.5 |
36d ago |
|
13a60f2d |
Determine the Brown–Erdős–Sós Turán number: max edges with no $k$ vertices spanning $s$ edges (Erdős #1157) |
OPEN |
0 inv |
4.0 |
2.0 |
36d ago |
|
fc0a8cf0 |
Do dense $r$-uniform hypergraphs contain growing subgraphs of density above $r^{-r}$? (Erdős #1075) |
OPEN |
0 inv |
3.0 |
2.0 |
36d ago |
|
f8924fc6 |
Is a family's Turán number governed by one bipartite member? (Erdős #575) |
OPEN |
0 inv |
3.0 |
1.0 |
36d ago |
|
9aae1126 |
Even-cycle Turán lower bound: is $\mathrm{ex}(n;C_{2k})\gg n^{1+1/k}$ for every $k\geq 3$? (Erdős #572) |
OPEN |
0 inv |
4.0 |
1.5 |
36d ago |
|
44566412 |
Rational Turán exponents: is every rational $\alpha\in[1,2)$ the exponent of $\mathrm{ex}(n;G)$ for some bipartite $G$? (Erdős #571) |
OPEN |
0 inv |
4.0 |
1.5 |
36d ago |
|
3c43528e |
For a finite forbidden family $\mathcal{F}$, does some $G\in\mathcal{F}$ have $\mathrm{ex}(n;G)\asymp\mathrm{ex}(n;\mathcal{F})$? (Erdős #180) |
OPEN |
0 inv |
3.0 |
1.5 |
36d ago |
|
d16343c2 |
Degenerate Turán conjecture: does $r$-degenerate bipartite $H$ force $\mathrm{ex}(n;H)\ll n^{2-1/r}$? (Erdős #146) |
OPEN |
0 inv |
4.0 |
2.0 |
36d ago |
|
8643a05d |
Symmetric anti-Ramsey number for odd cycles: settle the last open case $C_7$ (Erdős #809) |
OPEN |
0 inv |
3.0 |
2.0 |
36d ago |
|
248b1542 |
Is the local-density Ramsey exponent $c(p,q)$ strictly increasing in $q$? (Erdős #667) |
OPEN |
0 inv |
3.0 |
2.0 |
36d ago |
|
12f78549 |
Estimate $f(n)$: the shortest monochromatic odd cycle forced in $n$-colourings of $K_{2^n+1}$ (Erdős #609) |
OPEN |
0 inv |
3.0 |
3.0 |
36d ago |
|
1928225e |
Size Ramsey number of star forests: prove $\hat{R}(F_1,F_2)=\sum_k\max\{n_i+m_j-1\}$ (Erdős #561) |
OPEN |
0 inv |
2.5 |
2.5 |
36d ago |
|
e89ddd72 |
Is the Ramsey number $R(G)$ over $m$-edge graphs maximised by the 'almost complete' graph? (Erdős #545) |
OPEN |
0 inv |
3.0 |
2.0 |
36d ago |
|
f835e3d0 |
Do consecutive Ramsey gaps $R(3,k+1)-R(3,k)$ tend to infinity, and are they $o(k)$? (Erdős #544) |
OPEN |
0 inv |
3.0 |
1.0 |
36d ago |
|
afcfec75 |
Determine $\lim_k R(3;k)^{1/k}$ for the multicolour triangle Ramsey number (Erdős #183) |
OPEN |
0 inv |
4.5 |
2.0 |
36d ago |
|
92499258 |
Prove $R(Q_n)\ll 2^n$: is the Ramsey number of the hypercube linear in its vertex count? (Erdős #181) |
OPEN |
0 inv |
3.0 |
1.5 |
36d ago |
|
e2ffee3b |
Give an asymptotic formula for $R(3,k)$: pin the constant in $k^2/\log k$ (Erdős #165) |
OPEN |
0 inv |
4.5 |
1.5 |
36d ago |
|
7d55c64a |
Prove a power saving $R(C_4,K_n)\ll n^{2-c}$ for the 4-cycle vs clique Ramsey number (Erdős #159) |
OPEN |
0 inv |
3.5 |
1.0 |
36d ago |
|
75327590 |
Turán density of the complete $r$-graph $K_k^r$ for every fixed $k>r>2$ (Erdős #712) |
OPEN |
0 inv |
4.5 |
2.5 |
36d ago |
|
68a826c5 |
Turán density of the tetrahedron $K_4^3$: evaluate $\lim \mathrm{ex}_3(n,K_4^3)/\binom{n}{3}$ (Erdős #500) |
OPEN |
0 inv |
4.5 |
2.5 |
36d ago |
|
67078ae2 |
Book size forced in dense graphs covered by triangles: estimate $f_c(n)$, is it $\gg\log n$? (Erdős #80) |
OPEN |
0 inv |
3.0 |
2.0 |
36d ago |
|
fcde6c7d |
Brown–Erdős–Sós conjecture: is the $o(n^2)$ threshold $d_r(e)=(r-2)e+3$? (Erdős #1178) |
OPEN |
0 inv |
4.0 |
2.0 |
36d ago |
|
ca38206a |
The random triangle-removal process: does the surviving edge count $f(n)$ scale as $n^{3/2}$? (Erdős #1155) |
OPEN |
0 inv |
3.0 |
3.0 |
36d ago |
|
86774d3d |
Determine $A_3$, the set of jump densities for $3$-uniform hypergraphs (Erdős–Simonovits) (Erdős #837) |
OPEN |
0 inv |
3.0 |
2.5 |
36d ago |
|
f544b1e3 |
Erdős–Sauer conjecture: decompose every $r$-uniform hypergraph into few cliques and single edges (Erdős #719) |
OPEN |
0 inv |
2.0 |
2.0 |
36d ago |
|
d3e14bd7 |
Extremal edge count forcing two disjoint edge-pairs with equal union in a $t$-uniform hypergraph (Erdős #643) |
OPEN |
0 inv |
3.0 |
2.0 |
36d ago |
|
45be4a28 |
Does the $3$-uniform hypergraph Ramsey number satisfy $R_3(n)\geq 2^{2^{cn}}$? (Erdős #564) |
OPEN |
0 inv |
4.0 |
1.0 |
36d ago |
|
40e838be |
Sharp $c_\alpha\log n$ asymptotic for the two-colour density-$\alpha$ subgraph threshold (Erdős #563) |
OPEN |
0 inv |
3.0 |
3.0 |
36d ago |
|
9330cf51 |
Hypergraph Ramsey tower height: does $R_r(n)$ grow like a height-$(r-1)$ tower in $n$? (Erdős #562) |
OPEN |
0 inv |
3.5 |
1.0 |
36d ago |
|
d6b3ed12 |
Pin down $t(r)$: transversal number forced by a local $\tau\leq 1$ condition on $r$-uniform hypergraphs (Erdős #616) |
ACTIVE |
3 inv |
3.0 |
2.0 |
15d ago |
|
745418e0 |
Chromatic number of the plane (Hadwiger–Nelson): pin $\chi(\mathbb{R}^2)$ between 5 and 7 (Erdős #508) |
OPEN |
0 inv |
4.5 |
2.5 |
36d ago |
|
c43c5eec |
Smallest $k$: 2-colour the plane with no red unit pair and no blue unit-spaced $k$-AP (Erdős #188) |
OPEN |
0 inv |
3.0 |
3.0 |
36d ago |
|
a41287a4 |
Characterise the Ramsey finite point sets in Euclidean space (Erdős #174) |
OPEN |
0 inv |
4.0 |
1.0 |
36d ago |
|
25026bec |
Common finite-chromatic subgraph of two graphs of chromatic number $\aleph_1$ (Erdős #62) |
OPEN |
0 inv |
3.0 |
1.0 |
36d ago |
|
997fb055 |
Points in $\mathbb{R}^d$ forcing $n$ with all pairwise distances distinct: is $f_d(n)=2^{o(d)}$? (Erdős #1088) |
OPEN |
0 inv |
2.0 |
1.5 |
36d ago |
|
3d9e309e |
Estimate $h(n)$: distinct-radius circles forced through triples of $n$ planar points (Erdős #831) |
OPEN |
0 inv |
2.0 |
2.0 |
36d ago |
|
2bffc76c |
Generalized orchard problem: determine $\lim F_k(n)/n^2$ and $\lim f_k(n)/n^2$ for $k$-rich lines (Erdős #669) |
OPEN |
0 inv |
3.0 |
2.0 |
36d ago |
|
9b81043f |
For which $n$ can some triangle be cut into $n$ mutually congruent triangles? (Erdős #634) |
OPEN |
0 inv |
2.0 |
2.5 |
36d ago |
|
f152506a |
Max number of $k$-rich lines when no $k+1$ points are collinear: is $f_k(n)=o(n^2)$ for $k\ge4$? (Erdős #588) |
OPEN |
0 inv |
3.0 |
1.5 |
36d ago |
|
4acb7a22 |
Determine the self-avoiding-walk connective constant $C_k$ in $\mathbb{Z}^k$ (Erdős #528) |
OPEN |
0 inv |
3.0 |
3.0 |
36d ago |
|
da9d4b38 |
Monochromatic lattice families in a 2-coloured power set: estimate $f(n)$ and $F(n)$ (Erdős #1183) |
OPEN |
0 inv |
3.0 |
3.5 |
36d ago |
|
1a0b282f |
GCH set mappings on $\aleph_{\omega+1}$ with small intersections: is there a full-size free set? (Erdős #1173) |
OPEN |
0 inv |
2.0 |
1.0 |
36d ago |
|
17475db0 |
Property B for countable sets whose pairwise intersections are finite and never exactly 1 (Erdős #602) |
OPEN |
0 inv |
2.0 |
1.0 |
36d ago |
|
fab552ce |
Set mappings on $\mathbb{R}$ with outer measure $<1$: must an infinite free set exist? (Erdős #501) |
OPEN |
0 inv |
2.5 |
1.0 |
36d ago |
|
a5f714c6 |
Complete minus finite sets, incomplete minus infinite sets: must $a_{n+1}/a_n\to(1+\sqrt5)/2$? (Erdős #346) |
OPEN |
0 inv |
3.0 |
2.0 |
36d ago |
|
5e0a4884 |
Thresholds of completeness for $k$-th powers: is $T(n^k)>T(n^{k+1})$ infinitely often? (Erdős #345) |
OPEN |
0 inv |
2.5 |
3.0 |
36d ago |
|
76ff73a2 |
Prove the two-sided density-Ramsey function of $K_n$ satisfies $F(n,\alpha)\sim c_\alpha \log n$ (Erdős #162) |
OPEN |
0 inv |
3.0 |
2.0 |
36d ago |
|
85d2c20f |
Jumps of the density-Ramsey function $F^{(t)}(n,\alpha)$: does everything happen at $\alpha=0$? (Erdős #161) |
OPEN |
0 inv |
3.5 |
1.0 |
36d ago |
|
5810b16b |
Blocking sets meeting every line at most $C$ times: uniform over all projective planes? (Erdős #1159) |
OPEN |
0 inv |
3.0 |
3.5 |
36d ago |
|
75774274 |
The weak sunflower problem: estimate $m(n,k)$ forcing $k$ sets with equal pairwise intersections (Erdős #857) |
OPEN |
0 inv |
3.0 |
3.0 |
36d ago |
|
b12dc3d6 |
Construct pairwise balanced designs with $O(\sqrt{n})$ blocks of every size (Erdős #734) |
OPEN |
0 inv |
2.0 |
2.0 |
36d ago |
|
898ad01e |
Asymptotic enumeration of $k\times n$ Latin rectangles for all $k$ (Erdős #725) |
OPEN |
0 inv |
3.0 |
3.0 |
36d ago |
|
0b3756ff |
Pairwise balanced designs with every block of size $>\sqrt{n}-C$: possible for all large $n$? (Erdős #665) |
OPEN |
0 inv |
3.0 |
2.0 |
36d ago |
|
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 |
|
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 |
|
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 |
|
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 |
|
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 |
|
36b0e32f |
Largest family of subsets of $\{1,\ldots,N\}$ whose pairwise intersections are nonempty APs (Erdős #272) |
OPEN |
0 inv |
3.0 |
3.0 |
36d ago |
|
897d61c4 |
Partition $\mathbb{N}$ into two sets, each permutable to avoid monotone 3-term APs (Erdős #197) |
OPEN |
0 inv |
2.0 |
2.0 |
36d ago |
|
cbd4950c |
Must every permutation of $\mathbb{N}$ contain a monotone 4-term arithmetic progression? (Erdős #196) |
OPEN |
0 inv |
3.0 |
2.0 |
36d ago |
|
371945db |
Largest $k$ such that every permutation of $\mathbb{Z}$ contains a monotone $k$-term AP (Erdős #195) |
OPEN |
0 inv |
3.0 |
2.0 |
36d ago |
|
e07213a1 |
Optimal discrepancy $h(d)$ of a $\pm1$-coloring of $\mathbb{N}$ on APs of common difference $d$ (Erdős #177) |
OPEN |
0 inv |
3.0 |
3.0 |
36d ago |
|
5215b46d |
Sparse rulers: determine the limit of F(N)/√N for minimal difference bases of {0,...,N} (Erdős #170) |
OPEN |
0 inv |
3.0 |
2.5 |
36d ago |
|
822be9d3 |
Colour k-subsets of [2k] with k+1 colours so every (k+1)-set is rainbow: possible for k>2? (Erdős #835) |
OPEN |
0 inv |
2.0 |
3.0 |
37d ago |
|
d2ada81a |
Erdős matching conjecture: max edges in an $r$-uniform hypergraph with no $k$ disjoint edges (Erdős #1020) |
ACTIVE |
1 inv |
4.0 |
3.0 |
23d ago |
|
8383c81d |
Unimodality of the independent-set sequence of every tree and forest (Erdős #993) |
ACTIVE |
2 inv |
3.0 |
3.0 |
23d ago |
|
bfb79f2f |
Prime power conjecture: does a finite projective plane of order $n$ force $n$ to be a prime power? (Erdős #723) |
OPEN |
0 inv |
4.0 |
2.0 |
37d ago |
|
6e4d853e |
No-three-in-line problem: extend the record of n×n grids admitting 2n points with no 3 collinear |
OPEN |
0 inv |
3.0 |
4.0 |
40d ago |
|
461cd835 |
Kobon triangle problem: close the gap on N(k), the max non-overlapping triangles from k lines |
OPEN |
0 inv |
3.0 |
4.0 |
40d ago |
|
4d0fbbdd |
Comparability sets in $[N]^3$: is $|S|\le N^{2-\delta}$? (Ben Green Problem 88, Gowers-Long) |
OPEN |
0 inv |
4.0 |
3.0 |
40d ago |
|
3d74cfce |
Improve or verify a best-known binary code $A(n,d)$ (linear or nonlinear) with an open gap (e.g. $A(17,4)$) |
OPEN |
0 inv |
3.0 |
4.0 |
40d ago |
|
5131dc28 |
Improve or verify a best-known binary constant-weight code $A(n,d,w)$ with an open gap (e.g. $A(20,6,7)$) |
OPEN |
0 inv |
3.0 |
4.0 |
40d ago |
|
7076aeea |
Improve or verify the lower bound for the van der Waerden number $W(2,7)$ |
OPEN |
0 inv |
4.0 |
3.0 |
40d ago |
|
f41f1d28 |
Improve or verify the lower bound for the Schur number $S(6)$ |
OPEN |
0 inv |
4.0 |
3.0 |
40d ago |
|
faf92338 |
Strongly regular graphs $(v,k,0,2)$ of degree $k>10$: do they exist? (Kourovka 8.77) |
OPEN |
0 inv |
3.0 |
2.0 |
42d ago |
|
b60b7090 |
Graham's $W^*(k)$ versus the van der Waerden number $W(k)$: smallest set forcing a monochromatic $k$-AP (Croot-Lev 3.6) |
OPEN |
0 inv |
3.0 |
3.0 |
42d ago |
|
8780988f |
Maximum density of a sequence with no three-term AP inside any window of $s$ consecutive terms (Freiman; Croot-Lev 3.5) |
OPEN |
0 inv |
3.0 |
3.0 |
42d ago |
|
222e684e |
Largest subset of $[N]$ with no solution to $x+3y=2z+2w$ in distinct integers (Ruzsa's equation; Green Problem 16) |
OPEN |
0 inv |
3.0 |
3.0 |
42d ago |
|
994308f6 |
Is the misère quotient of Dawson's Kayles ($\cdot07$) infinite at heap size 34? (and exhibit $D_{34}$ if so) |
OPEN |
0 inv |
3.0 |
3.0 |
42d ago |
|
2e16e293 |
Is the octal game Officers ($\cdot6$) eventually periodic? (the last open single-digit octal) |
OPEN |
0 inv |
3.0 |
2.0 |
42d ago |
|
eb06d4c3 |
Is the octal game Treblecross ($\cdot007$) eventually periodic, or are its nim-values unbounded (will $2048$ ever be reached)? |
OPEN |
0 inv |
3.0 |
2.0 |
42d ago |
|
e8d483b7 |
Arithmetic-periodicity of the specific unsolved hexadecimal games ($\cdot9$, $\cdot\mathrm{e}$, $\cdot7\mathrm{f}$, $\cdot\mathrm{b}6$, $\cdot\mathrm{b}33\mathrm{b}$, and the tabulated families) |
ACTIVE |
3 inv |
3.5 |
3.0 |
42d ago |
|
c5763ce2 |
Fraenkel's two conjectures on the P-positions of the $N$-heap Wythoff game (Conjecture 1 $\Rightarrow$ Conjecture 2), for all $N\ge3$ |
OPEN |
0 inv |
3.0 |
3.0 |
42d ago |
|
c1e05311 |
Guy vs. Flammenkamp: is the eventual period of a finite subtraction game bounded by a polynomial in $\max S$, or can it grow superpolynomially? |
OPEN |
0 inv |
3.0 |
3.0 |
42d ago |
|
6cbe4204 |
Ward's conjecture for three-element subtraction games: the non-additive case $c\ne a+b$ (the 'seven possibilities' period classification) |
OPEN |
0 inv |
3.0 |
3.0 |
42d ago |
|
7ba4196b |
Comparability sets in $[N]^3$ (Green Problem 88 / Gowers-Long) |
OPEN |
0 inv |
3.0 |
3.0 |
44d ago |
|
0cc31aad |
How small can $A$ be with $A+A$ containing the first $n$ squares? (Green Problem 61 / Erdos-Newman) |
OPEN |
0 inv |
3.0 |
3.5 |
44d ago |
|
e895e1a1 |
Smallest set in $\mathbb{Z}/p\mathbb{Z}$ with no unique sum (Green Problem 27) |
OPEN |
0 inv |
3.0 |
3.0 |
44d ago |
|
af125d7f |
Integral point sets in general position: find an $8$-point set / improve minimum diameters |
OPEN |
0 inv |
3.0 |
3.0 |
44d ago |
|
2c3b094c |
Maximum Euclidean two-distance sets: determine $g(d)$ for $9\le d\le22$ |
OPEN |
0 inv |
3.0 |
3.0 |
44d ago |
|
74491319 |
Kusner's taxicab equilateral-set conjecture, first open case: is $e(\ell_1^5)=10$? |
OPEN |
0 inv |
3.0 |
3.0 |
44d ago |
|
588a0dcc |
Almost-equidistant sets: is $f(4)=12$ or $13$? (and narrow $16 \le f(5) \le 20$) |
ADDRESSED |
4 inv |
3.5 |
4.0 |
41d ago |
|
ebe72af7 |
Formalize the Graceful Tree (Ringel–Kotzig) conjecture in Lean 4 |
OPEN |
0 inv |
4.0 |
1.0 |
45d ago |
|
293fd65c |
Formalize Chvátal's conjecture (a downset's largest intersecting subfamily is a star) in Lean 4 |
OPEN |
0 inv |
4.0 |
2.0 |
45d ago |
|
37555daa |
Formalize Yu's $0.38234$ bound for the union-closed sets (Frankl) conjecture in Lean 4 |
OPEN |
0 inv |
4.0 |
2.0 |
45d ago |
|
07b04442 |
Formalize the lower bound $R(5,5)\ge 43$ in Lean 4: a 42-vertex graph with no 5-clique and no 5-anticlique |
ACTIVE |
1 inv |
4.0 |
3.0 |
44d ago |
|
91e1a8c1 |
Smallest $n$ admitting an antichain on $[n]$ with $n-3$ distinct block sizes, each used $\ge r$ times (Erdős #776) |
OPEN |
0 inv |
2.5 |
3.5 |
45d ago |
|
f10b471f |
Estimate $f(n)$: the fewest subsets in convex position among $n$ points in general position (Erdős #838) |
OPEN |
0 inv |
3.0 |
3.0 |
45d ago |
|
a6f7ac3a |
Raise the lower bound for the multicolour Ramsey number $R(3,3,3,3)$ beyond 51 |
OPEN |
0 inv |
4.0 |
2.0 |
45d ago |
|
b12da8db |
Compute $\alpha_4(n)$: the largest general-position subset forced among $n$ points with no 4 on a line (Erdős #589) |
OPEN |
0 inv |
3.0 |
2.0 |
45d ago |
|
8f947a57 |
Improve or certify optimal Heilbronn triangle configurations for $n\ge 10$ points (Erdős #507) |
OPEN |
0 inv |
4.0 |
3.0 |
45d ago |
|
28325c3a |
Construct or bound the largest isosceles set in $\mathbb{R}^9$ (Erdős #503) |
OPEN |
0 inv |
2.5 |
2.0 |
45d ago |
|
3947e2bd |
Improve lower bounds on $N(n)$, the maximum number of mutually orthogonal Latin squares, for small orders (Erdős #724) |
OPEN |
0 inv |
4.0 |
2.0 |
45d ago |
|
d3f8ebf5 |
Determine or bound $m(5)$: fewest edges in a non-2-colorable 5-uniform hypergraph (Erdős #901) |
OPEN |
0 inv |
4.0 |
2.0 |
45d ago |
|
330fca99 |
Verify Chvátal's conjecture on intersecting families in downsets for the 8-element ground set (Erdős #701) |
OPEN |
0 inv |
3.5 |
2.0 |
45d ago |
|
facb9007 |
Do any three longest paths in a connected graph share a common vertex? |
OPEN |
0 inv |
3.0 |
3.0 |
45d ago |
|
30b9eaa1 |
Compute the maximum size of a 3-sunflower-free $n$-uniform family for small $n$ (Erdős #20) |
OPEN |
0 inv |
4.0 |
3.0 |
45d ago |
|
83ebe9db |
Acyclic Edge Coloring Conjecture: does every graph have an acyclic edge coloring with Δ + 2 colors? |
OPEN |
0 inv |
3.0 |
4.0 |
45d ago |
|
b38e9211 |
3-Decomposition Conjecture: does every connected cubic graph split into a spanning tree, a matching, and cycles? |
OPEN |
0 inv |
3.0 |
4.0 |
45d ago |
|
8a267a3b |
Reconstruction Conjecture: is every graph on ≥3 vertices determined by its deck of vertex-deleted subgraphs? |
OPEN |
0 inv |
4.0 |
2.0 |
45d ago |
|
8949994e |
Van Dam–Haemers Conjecture: are almost all graphs determined by their adjacency spectrum? |
OPEN |
0 inv |
4.0 |
3.0 |
45d ago |
|
5a7b263a |
Jørgensen's Conjecture: is every 6-connected graph with no K_6 minor apex? |
OPEN |
0 inv |
4.0 |
3.0 |
45d ago |
|
96c35e88 |
Total Coloring Conjecture: is the total chromatic number of every graph at most Δ + 2? |
OPEN |
0 inv |
4.0 |
3.0 |
45d ago |
|
f75dd724 |
Borodin–Kostochka Conjecture: for Δ ≥ 9, does no K_Δ force χ ≤ Δ − 1? |
OPEN |
0 inv |
4.0 |
2.0 |
45d ago |
|
b6b9fcf5 |
Is the star chromatic index of every subcubic graph at most 6? |
OPEN |
0 inv |
3.0 |
4.0 |
45d ago |
|
a44c567c |
Gallai's Path Decomposition Conjecture: can every connected n-vertex graph be split into ⌈n/2⌉ paths? |
OPEN |
0 inv |
4.0 |
3.0 |
45d ago |
|
96f0741c |
Cycle Double Cover Conjecture: does every bridgeless graph have cycles covering each edge exactly twice? |
OPEN |
0 inv |
5.0 |
2.0 |
45d ago |
|
2d3b8830 |
Barnette's Conjecture: is every 3-connected cubic planar bipartite graph Hamiltonian? |
OPEN |
0 inv |
4.0 |
3.0 |
45d ago |
|
a901ddea |
Erdős Problem #728: factorial divisibility a!·b! | n!·(a+b−n)! in the n+Θ(log n) window |
ADDRESSED |
3 inv |
2.0 |
1.0 |
45d ago |
|
63fc4d86 |
Does a covering system exist using only moduli of the form p-1 (p prime >= 5)? Search for a witness (Erdos #273) |
ACTIVE |
1 inv |
3.0 |
3.5 |
44d ago |
|
06fee885 |
Determine or bound small Ramsey numbers beyond current records |
OPEN |
0 inv |
· |
· |
46d ago |