Question

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

score 375 · Answer 1 · 2026-03-25 20:41:47

375

Views

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

Published on 25 Mar 2026 - 20:41

score 65 · Answer 2 · 2026-03-25 16:01:43

65

Views

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

Published on 25 Mar 2026 - 16:01

score 942 · Answer 3 · 2026-03-25 15:58:26

942

Views

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

Published on 25 Mar 2026 - 15:58

score 101 · Answer 4 · 2026-04-11 02:06:22

101

Views

Mutual independence in the Local Lemma

Published on 11 Apr 2026 - 2:06

score 328 · Answer 5 · 2026-03-25 16:03:01

328

Views

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

Published on 25 Mar 2026 - 16:03

score 101 · Answer 6 · 2026-04-26 06:15:02

101

Views

Probabilistic Number Theory

Published on 26 Apr 2026 - 6:15

score 171 · Answer 7 · 2026-04-28 13:41:23

171

Views

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

Published on 28 Apr 2026 - 13:41

score 75 · Answer 8 · 2026-04-27 17:11:35

75

Views

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

Published on 27 Apr 2026 - 17:11

score 48 · Answer 9 · 2026-05-10 23:29:41

48

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 10 May 2026 - 23:29

score 96 · Answer 10 · 2026-03-25 17:42:16

96

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 25 Mar 2026 - 17:42

score 33 · Answer 11 · 2026-03-25 17:42:05

33

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 25 Mar 2026 - 17:42

score 73 · Answer 12 · 2026-03-25 16:03:09

73

Views

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

Published on 25 Mar 2026 - 16:03

score 37 · Answer 13 · 2026-03-25 19:10:10

37

Views

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

Published on 25 Mar 2026 - 19:10

score 59 · Answer 14 · 2026-03-25 17:40:30

59

Views

A step in the proof of Erdos-Tetali Lemma.

Published on 25 Mar 2026 - 17:40

score 193 · Answer 15 · 2026-04-11 00:57:49

193

Views

Number of triangles in a random graph.

Published on 11 Apr 2026 - 0:57

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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