Question

Given an undirected graph with m edges, there is a cut with value strictly bigger than /2.

score 374 · Answer 1 · 2020-04-07 19:14:30

374

Views

Given an undirected graph with m edges, there is a cut with value strictly bigger than /2.

Published on 07 Apr 2020 - 19:14

score 64 · Answer 2 · 2020-04-09 03:54:44

64

Views

Suppose that $G$ is a $n$-vertex graph with $e(G)=\Theta(n^2)$ edges.

Published on 09 Apr 2020 - 3:54

score 941 · Answer 3 · 2020-04-16 00:23:07

941

Views

Show that $p^*(n)=n^{-2/3}$ is the threshold function

Published on 16 Apr 2020 - 0:23

score 99 · Answer 4 · 2020-04-18 18:37:11

99

Views

Mutual independence in the Local Lemma

Published on 18 Apr 2020 - 18:37

score 327 · Answer 5 · 2020-04-24 18:59:20

327

Views

Let $G$ be an $n$-vertex graph with at most $100n$ triangles. Prove that $G$ has a triangle-free...

Published on 24 Apr 2020 - 18:59

score 88 · Answer 6 · 2026-03-25 02:37:32

88

Views

Probabilistic Number Theory

Published on 25 Mar 2026 - 2:37

score 155 · Answer 7 · 2026-03-25 05:54:02

155

Views

probabilistic method:exercise using $\epsilon$-net and VC dimension

Published on 25 Mar 2026 - 5:54

score 61 · Answer 8 · 2026-03-24 22:40:22

61

Views

probabilistic method exercise: $\epsilon$-nets: Show difference of two triangles contains a random point

Published on 24 Mar 2026 - 22:40

score 46 · Answer 9 · 2020-05-14 16:31:09

46

Views

In a random graph $G(n,p)$ with $\delta(G) \geq \delta$, how is the event $\{S \subset V \text{ is not a dominating set} \}$ characterized?

Published on 14 May 2020 - 16:31

score 95 · Answer 10 · 2020-06-01 16:24:34

95

Views

Given $372$ points in a circle with a radius of $10$, there is an annulus with radii $2$ and $3$ containing at least $12$ of these points.

Published on 01 Jun 2020 - 16:24

score 32 · Answer 11 · 2020-06-05 10:06:20

32

Views

For $G \sim G(n, 0.5)$, $I$ a $k$-set of vertices, and event $E_I = \{G[I] \cong K_k \text{ or } K_k^c \}$, how many events does $E_I$ depend on?

Published on 05 Jun 2020 - 10:06

score 72 · Answer 12 · 2020-06-06 15:24:27

72

Views

How to show $p^3 \approx e^{-p{k \choose 2}}$ implies $p \approx \frac{12\ln(k)}{k^2}$?

Published on 06 Jun 2020 - 15:24

score 36 · Answer 13 · 2020-06-13 17:46:33

36

Views

What are some bounds on the size of largest subinterval in a random partition of the unit interval?

Published on 13 Jun 2020 - 17:46

score 58 · Answer 14 · 2020-06-13 22:32:44

58

Views

A step in the proof of Erdos-Tetali Lemma.

Published on 13 Jun 2020 - 22:32

score 191 · Answer 15 · 2020-06-22 22:05:34

191

Views

Number of triangles in a random graph.

Published on 22 Jun 2020 - 22:05

List Question

Given an undirected graph with m edges, there is a cut with value strictly bigger than /2.

Suppose that $G$ is a $n$-vertex graph with $e(G)=\Theta(n^2)$ edges.

Show that $p^*(n)=n^{-2/3}$ is the threshold function

Mutual independence in the Local Lemma

Let $G$ be an $n$-vertex graph with at most $100n$ triangles. Prove that $G$ has a triangle-free...

Probabilistic Number Theory

probabilistic method:exercise using $\epsilon$-net and VC dimension

probabilistic method exercise: $\epsilon$-nets: Show difference of two triangles contains a random point

In a random graph $G(n,p)$ with $\delta(G) \geq \delta$, how is the event $\{S \subset V \text{ is not a dominating set} \}$ characterized?

Given $372$ points in a circle with a radius of $10$, there is an annulus with radii $2$ and $3$ containing at least $12$ of these points.

For $G \sim G(n, 0.5)$, $I$ a $k$-set of vertices, and event $E_I = \{G[I] \cong K_k \text{ or } K_k^c \}$, how many events does $E_I$ depend on?

How to show $p^3 \approx e^{-p{k \choose 2}}$ implies $p \approx \frac{12\ln(k)}{k^2}$?

What are some bounds on the size of largest subinterval in a random partition of the unit interval?

A step in the proof of Erdos-Tetali Lemma.

Number of triangles in a random graph.

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