Question

Canonical Ramsey theorem in $m$-uniform setting admits $2^m$ canonical colorings.

score 66 · Answer 1 · 2026-05-10 17:16:03

66

Views

Canonical Ramsey theorem in $m$-uniform setting admits $2^m$ canonical colorings.

Published on 10 May 2026 - 17:16

score 70 · Answer 2 · 2026-05-10 14:32:16

70

Views

For $t \geq 3$, if $n \geq R^{(3)}(t,t)$, then n points in $\mathbb{R}^2$ always contain either t collinear points, or t points in convex position.

Published on 10 May 2026 - 14:32

score 807 · Answer 3 · 2026-04-16 20:07:59

Give a 13x13 square table. Colour S squares in the table such that no four coloured squares are the four vertices of a rectangle. Find maxS.

score 86 · Answer 4 · 2026-05-10 16:14:47

86

Views

Maximal subset with given Hamming distances

Published on 10 May 2026 - 16:14

score 55 · Answer 5 · 2026-05-11 00:39:04

55

Views

Relatively maximal sum-free subsets in finite groups

Published on 11 May 2026 - 0:39

score 95 · Answer 6 · 2026-05-10 18:27:48

95

Views

Cups and caps inequality: $f(s,t) \leq {s+t-2 \choose {s-2}}+1$

Published on 10 May 2026 - 18:27

score 109 · Answer 7 · 2026-05-10 23:31:41

109

Views

Show that a 3-uniform hypergraph on $n \geq 5$ points, in which each pair of points occurs in the same (positive) number of edges, is not 2-colorable.

Published on 10 May 2026 - 23:31

score 68 · Answer 8 · 2026-05-10 23:31:44

68

Views

Parameter $d$ that makes the probability of the graph $G(n,\frac{d}{n})$ being $k$-colorable tends to $0$, as $n \to \infty$ , for $k \leq 2$.

Published on 10 May 2026 - 23:31

score 38 · Answer 9 · 2026-04-16 01:43:52

38

Views

$S = \{1,2,...,2005\}$, $A = \{a_{1}, ..., a_{k}\} \subset S$ with $a_{i}+a_{j}$ not multiple of 125. What is $\max(k)$?

Published on 16 Apr 2026 - 1:43

score 540 · Answer 10 · 2026-04-13 12:03:55

540

Views

Large subgroups of Symmetric Group

Published on 13 Apr 2026 - 12:03

score 135 · Answer 11 · 2026-04-15 16:53:09

135

Views

Say a finite set $M$ has two partition $A_1,A_2,...A_p$ and $B_1,B_2,...B_p$ such that ...

Published on 15 Apr 2026 - 16:53

score 68 · Answer 12 · 2026-05-10 23:31:36

68

Views

Show that, if girth$(G) \geq g, \text{and } \delta(G) \geq d$, then $|V(G)|= n = \Omega(d^k), \text{where } k = \lfloor \frac{g-1}{2} \rfloor$.

Published on 10 May 2026 - 23:31

score 384 · Answer 13 · 2026-03-26 04:35:06

384

Views

Maximizing $\sum_{i,j=1}^{n}|\operatorname{deg}\ x_{i}-\operatorname{deg}\ x_{j}|^{3}$ over all simple graphs with $n$ vertices

Published on 26 Mar 2026 - 4:35

score 110 · Answer 14 · 2026-05-10 23:20:36

110

Views

Simplification of the $\epsilon$-regularity condition in graphs.

Published on 10 May 2026 - 23:20

score 318 · Answer 15 · 2026-05-10 23:30:40

318

Views

If each edge of a graph $G=(V,E)$ belongs to exactly one triangle then $|E|=\omicron(n^{2})$.

Published on 10 May 2026 - 23:30

List Question

Canonical Ramsey theorem in $m$-uniform setting admits $2^m$ canonical colorings.

For $t \geq 3$, if $n \geq R^{(3)}(t,t)$, then n points in $\mathbb{R}^2$ always contain either t collinear points, or t points in convex position.

Give a 13x13 square table. Colour S squares in the table such that no four coloured squares are the four vertices of a rectangle. Find maxS.

Maximal subset with given Hamming distances

Relatively maximal sum-free subsets in finite groups

Cups and caps inequality: $f(s,t) \leq {s+t-2 \choose {s-2}}+1$

Show that a 3-uniform hypergraph on $n \geq 5$ points, in which each pair of points occurs in the same (positive) number of edges, is not 2-colorable.

Parameter $d$ that makes the probability of the graph $G(n,\frac{d}{n})$ being $k$-colorable tends to $0$, as $n \to \infty$ , for $k \leq 2$.

$S = \{1,2,...,2005\}$, $A = \{a_{1}, ..., a_{k}\} \subset S$ with $a_{i}+a_{j}$ not multiple of 125. What is $\max(k)$?

Large subgroups of Symmetric Group

Say a finite set $M$ has two partition $A_1,A_2,...A_p$ and $B_1,B_2,...B_p$ such that ...

Show that, if girth$(G) \geq g, \text{and } \delta(G) \geq d$, then $|V(G)|= n = \Omega(d^k), \text{where } k = \lfloor \frac{g-1}{2} \rfloor$.

Maximizing $\sum_{i,j=1}^{n}|\operatorname{deg}\ x_{i}-\operatorname{deg}\ x_{j}|^{3}$ over all simple graphs with $n$ vertices

Simplification of the $\epsilon$-regularity condition in graphs.

If each edge of a graph $G=(V,E)$ belongs to exactly one triangle then $|E|=\omicron(n^{2})$.

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