Question

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

score 64 · Answer 1 · 2020-01-26 19:38:07

64

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

Published on 26 Jan 2020 - 19:38

score 69 · Answer 2 · 2026-03-25 06:22:07

69

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 25 Mar 2026 - 6:22

score 804 · Answer 3 · 2020-01-29 02:41:25

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 84 · Answer 4 · 2020-01-29 19:03:37

84

Views

Maximal subset with given Hamming distances

Published on 29 Jan 2020 - 19:03

score 54 · Answer 5 · 2026-03-25 09:23:43

54

Views

Relatively maximal sum-free subsets in finite groups

Published on 25 Mar 2026 - 9:23

score 93 · Answer 6 · 2020-02-03 09:33:58

93

Views

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

Published on 03 Feb 2020 - 9:33

score 107 · Answer 7 · 2020-02-03 21:23:31

107

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 03 Feb 2020 - 21:23

score 67 · Answer 8 · 2026-03-25 14:25:27

67

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 25 Mar 2026 - 14:25

score 35 · Answer 9 · 2020-02-06 04:36:44

35

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 06 Feb 2020 - 4:36

score 537 · Answer 10 · 2020-02-06 16:45:05

537

Views

Large subgroups of Symmetric Group

Published on 06 Feb 2020 - 16:45

score 133 · Answer 11 · 2020-02-23 09:26:30

133

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 23 Feb 2020 - 9:26

score 66 · Answer 12 · 2020-02-24 15:55:28

66

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 24 Feb 2020 - 15:55

score 383 · Answer 13 · 2020-02-29 14:41:46

383

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 29 Feb 2020 - 14:41

score 108 · Answer 14 · 2020-03-01 21:09:56

108

Views

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

Published on 01 Mar 2020 - 21:09

score 316 · Answer 15 · 2020-03-02 15:23:29

316

Views

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

Published on 02 Mar 2020 - 15:23

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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