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048ca1fd |
Balanced $e(G)$-colourings of $K_n$: which graphs $G$ are forced to appear rainbow? (Erdős #811) |
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3.0 |
3.0 |
36d ago |
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abb27b3a |
Can a graph with $\epsilon n^2$ edges be $n$-coloured so every $C_4$ is rainbow? (Erdős #810) |
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3.0 |
2.0 |
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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8643a05d |
Symmetric anti-Ramsey number for odd cycles: settle the last open case $C_7$ (Erdős #809) |
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36d ago |
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248b1542 |
Is the local-density Ramsey exponent $c(p,q)$ strictly increasing in $q$? (Erdős #667) |
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2.0 |
36d ago |
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12f78549 |
Estimate $f(n)$: the shortest monochromatic odd cycle forced in $n$-colourings of $K_{2^n+1}$ (Erdős #609) |
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3.0 |
3.0 |
36d ago |
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589c2ced |
Do linear tree-Ramsey and quadratic clique-Ramsey together force Ramsey size-linearity? (Erdős #568) |
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1.0 |
36d ago |
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8243922c |
Ramsey size-linearity of $Q_3$, $K_{3,3}$, and the subdivided $K_4$: is $R(G,H)\ll m$? (Erdős #567) |
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36d ago |
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8a48a84f |
Is every graph whose $k$-vertex subgraphs have at most $2k-3$ edges Ramsey size-linear? (Erdős #566) |
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3.0 |
1.0 |
36d ago |
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1928225e |
Size Ramsey number of star forests: prove $\hat{R}(F_1,F_2)=\sum_k\max\{n_i+m_j-1\}$ (Erdős #561) |
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2.5 |
2.5 |
36d ago |
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c45beb19 |
Determine the size Ramsey number $\hat{R}(K_{n,n})$ of the complete bipartite graph (Erdős #560) |
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3.0 |
1.0 |
36d ago |
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e346503e |
Determine the multicolour Ramsey number $R_k(K_{s,t})$ of complete bipartite graphs (Erdős #558) |
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3.0 |
2.5 |
36d ago |
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5df8b87b |
Do multicolour Ramsey numbers of trees grow linearly: is $R_k(T)\leq kn+O(1)$? (Erdős #557) |
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3.0 |
2.0 |
36d ago |
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fbd34fd1 |
Determine the multicolour Ramsey number $R_k(C_{2n})$ of even cycles (Erdős #555) |
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3.0 |
2.5 |
36d ago |
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5c5fd7bb |
Multicolour Ramsey of odd cycles negligible vs triangles: $R_k(C_{2n+1})/R_k(K_3)\to0$ (Erdős #554) |
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3.0 |
1.0 |
36d ago |
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de1bde1f |
Determine the Ramsey number $R(C_4,S_n)$ of a 4-cycle versus a star (Erdős #552) |
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3.0 |
3.0 |
36d ago |
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e89ddd72 |
Is the Ramsey number $R(G)$ over $m$-edge graphs maximised by the 'almost complete' graph? (Erdős #545) |
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3.0 |
2.0 |
36d ago |
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f835e3d0 |
Do consecutive Ramsey gaps $R(3,k+1)-R(3,k)$ tend to infinity, and are they $o(k)$? (Erdős #544) |
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3.0 |
1.0 |
36d ago |
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afcfec75 |
Determine $\lim_k R(3;k)^{1/k}$ for the multicolour triangle Ramsey number (Erdős #183) |
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4.5 |
2.0 |
36d ago |
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92499258 |
Prove $R(Q_n)\ll 2^n$: is the Ramsey number of the hypercube linear in its vertex count? (Erdős #181) |
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3.0 |
1.5 |
36d ago |
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e2ffee3b |
Give an asymptotic formula for $R(3,k)$: pin the constant in $k^2/\log k$ (Erdős #165) |
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4.5 |
1.5 |
36d ago |
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7d55c64a |
Prove a power saving $R(C_4,K_n)\ll n^{2-c}$ for the 4-cycle vs clique Ramsey number (Erdős #159) |
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3.5 |
1.0 |
36d ago |
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50ff2c2a |
Determine the digraph Ramsey function $k(n,m)$: independent set vs transitive tournament (Erdős #112) |
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3.0 |
3.0 |
36d ago |
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a8284804 |
Independence number of planar minimum-distance-1 point sets: estimate $g(n)$ and $\lim g(n)/n$ (Erdős #1066) |
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3.0 |
3.0 |
36d ago |
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f862d502 |
Coprime graph of a dense subset of $[n]$: does the extremal threshold force all short odd cycles? (Erdős #883) |
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2.0 |
2.5 |
36d ago |
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75327590 |
Turán density of the complete $r$-graph $K_k^r$ for every fixed $k>r>2$ (Erdős #712) |
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4.5 |
2.5 |
36d ago |
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68a826c5 |
Turán density of the tetrahedron $K_4^3$: evaluate $\lim \mathrm{ex}_3(n,K_4^3)/\binom{n}{3}$ (Erdős #500) |
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4.5 |
2.5 |
36d ago |
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5161b7cf |
Does chromatic number $k$ force the Ramsey number $R(G)$ close to $R(k)$? (Erdős #87) |
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2.0 |
2.0 |
36d ago |
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67078ae2 |
Book size forced in dense graphs covered by triangles: estimate $f_c(n)$, is it $\gg\log n$? (Erdős #80) |
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3.0 |
2.0 |
36d ago |
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4a822fce |
Constructive exponential lower bound for Ramsey numbers: explicit graphs forcing $R(k)>C^k$ (Erdős #78) |
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3.5 |
1.5 |
36d ago |
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ebb7504d |
Determine the diagonal Ramsey growth constant $\lim_{k\to\infty} R(k)^{1/k}$ (Erdős #77) |
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4.5 |
1.0 |
36d ago |
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fcde6c7d |
Brown–Erdős–Sós conjecture: is the $o(n^2)$ threshold $d_r(e)=(r-2)e+3$? (Erdős #1178) |
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4.0 |
2.0 |
36d ago |
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ca38206a |
The random triangle-removal process: does the surviving edge count $f(n)$ scale as $n^{3/2}$? (Erdős #1155) |
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3.0 |
3.0 |
36d ago |
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86774d3d |
Determine $A_3$, the set of jump densities for $3$-uniform hypergraphs (Erdős–Simonovits) (Erdős #837) |
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3.0 |
2.5 |
36d ago |
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f544b1e3 |
Erdős–Sauer conjecture: decompose every $r$-uniform hypergraph into few cliques and single edges (Erdős #719) |
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2.0 |
2.0 |
36d ago |
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d3e14bd7 |
Extremal edge count forcing two disjoint edge-pairs with equal union in a $t$-uniform hypergraph (Erdős #643) |
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3.0 |
2.0 |
36d ago |
|
45be4a28 |
Does the $3$-uniform hypergraph Ramsey number satisfy $R_3(n)\geq 2^{2^{cn}}$? (Erdős #564) |
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4.0 |
1.0 |
36d ago |
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40e838be |
Sharp $c_\alpha\log n$ asymptotic for the two-colour density-$\alpha$ subgraph threshold (Erdős #563) |
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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) |
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3.5 |
1.0 |
36d ago |
|
87592d1b |
Must large chromatic number with no K_t force two anticomplete c-chromatic subgraphs? (Erdős #1111) |
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3.0 |
2.5 |
36d ago |
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b5105156 |
A minimum-degree threshold on 2^n vertices forcing the n-cube Q_n (Erdős #1035) |
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3.0 |
3.0 |
36d ago |
|
6c1038e9 |
Estimate h(n): largest guaranteed triangle degree-sum above the Turán threshold (Erdős #1033) |
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3.0 |
2.0 |
36d ago |
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cd278e5a |
Estimate f(n,k), the clique partition number for graphs with more than n²/4 edges (Erdős #1017) |
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3.0 |
2.0 |
36d ago |
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8f2f325f |
Determine h_3(k): fewest vertices in a triangle-free graph of chromatic number k (Erdős #1013) |
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3.0 |
2.5 |
36d ago |
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62208b79 |
Determine f_r(n): fewest edges forcing a triangle in an n-vertex graph of chromatic number ≥ r (Erdős #1011) |
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3.0 |
2.5 |
36d ago |
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7484ed39 |
Estimate h_t(d): fewest edges forcing two edges at distance ≥ t in a max-degree-d graph (Erdős #934) |
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3.0 |
3.0 |
36d ago |
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e36d5e7b |
Estimate f(n): fewest vertices in a tournament where every n vertices have a common dominator (Erdős #902) |
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3.0 |
2.0 |
36d ago |
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ae16c550 |
Erdős–Hajnal: clique size forced when every 7 vertices span a triangle — estimate $h(n)$ (Erdős #813) |
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3.0 |
2.0 |
36d ago |
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f4b54a16 |
Erdős–Hajnal: smallest $g(n)$ so every $g(n)$-subset has a $\log n$ clique and $\log n$ independent set (Erdős #805) |
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3.0 |
2.0 |
36d ago |
|
067f65f8 |
Independence number of $K_r$-free graphs: is the AEKS $\frac{\log t}{t}n$ bound true for all $r$? (Erdős #802) |
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4.0 |
1.0 |
36d ago |