Question

A graph $G(n,p)$ has $\Omega(k^2)$ edges of a special type, $k \in \mathbb{Z}^+$. If $p = \omega(k^{-2})$, then w.h.p. one of the edges is in $G$.

score 31 · Answer 1 · 2020-06-21 16:19:59

31

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A graph $G(n,p)$ has $\Omega(k^2)$ edges of a special type, $k \in \mathbb{Z}^+$. If $p = \omega(k^{-2})$, then w.h.p. one of the edges is in $G$.

Published on 21 Jun 2020 - 16:19

score 503 · Answer 2 · 2026-03-26 06:12:12

503

Views

zero-one-law in percolation theory

Published on 26 Mar 2026 - 6:12

score 192 · Answer 3 · 2026-03-25 15:59:22

192

Views

Number of triangles in a random graph.

Published on 25 Mar 2026 - 15:59

score 44 · Answer 4 · 2020-06-23 08:11:39

44

Views

Model Epidemic Random Graph

Published on 23 Jun 2020 - 8:11

score 229 · Answer 5 · 2026-03-25 19:04:23

229

Views

Interpretation of martingales in graphs.

Published on 25 Mar 2026 - 19:04

score 38 · Answer 6 · 2020-06-25 15:53:03

38

Views

Distance between two vertices from the ER graph.

Published on 25 Jun 2020 - 15:53

score 30 · Answer 7 · 2026-03-25 07:49:23

30

Views

Value $p$ that makes the random hypergraph $H^{(k)}(n,p)$ a good cover?

Published on 25 Mar 2026 - 7:49

score 168 · Answer 8 · 2020-06-29 03:00:45

168

Views

High probability range of chromatic number

Published on 29 Jun 2020 - 3:00

score 48 · Answer 9 · 2020-07-03 20:48:39

48

Views

Cover and fractional covers

Published on 03 Jul 2020 - 20:48

score 51 · Answer 10 · 2026-03-25 07:45:02

51

Views

Probability of a vertex not belonging to a set of edges in a random hypergraph.

Published on 25 Mar 2026 - 7:45

score 150 · Answer 11 · 2020-07-05 09:33:40

150

Views

Graphon model for random graphs and almost surely dense graphs

Published on 05 Jul 2020 - 9:33

score 56 · Answer 12 · 2020-07-06 10:01:41

56

Views

How many times does the graph of $x = t^2 - t - 6$, $y = 2t, -5 < t < 5$ cross the $y$-axis?

Published on 06 Jul 2020 - 10:01

score 264 · Answer 13 · 2026-03-26 19:00:54

264

Views

How do you mathematically define a random line or in general, a random subspace of a Euclidean space?

Published on 26 Mar 2026 - 19:00

score 487 · Answer 14 · 2026-03-25 23:39:08

487

Views

Why are the probability and mean number of edges between two nodes in a network equal for large networks?

Published on 25 Mar 2026 - 23:39

score 366 · Answer 15 · 2026-03-25 17:40:23

366

Views

Why the clique numbers of almost all graphs are concentrated at two values?

Published on 25 Mar 2026 - 17:40

List Question

A graph $G(n,p)$ has $\Omega(k^2)$ edges of a special type, $k \in \mathbb{Z}^+$. If $p = \omega(k^{-2})$, then w.h.p. one of the edges is in $G$.

zero-one-law in percolation theory

Number of triangles in a random graph.

Model Epidemic Random Graph

Interpretation of martingales in graphs.

Distance between two vertices from the ER graph.

Value $p$ that makes the random hypergraph $H^{(k)}(n,p)$ a good cover?

High probability range of chromatic number

Cover and fractional covers

Probability of a vertex not belonging to a set of edges in a random hypergraph.

Graphon model for random graphs and almost surely dense graphs

How many times does the graph of $x = t^2 - t - 6$, $y = 2t, -5 < t < 5$ cross the $y$-axis?

How do you mathematically define a random line or in general, a random subspace of a Euclidean space?

Why are the probability and mean number of edges between two nodes in a network equal for large networks?

Why the clique numbers of almost all graphs are concentrated at two values?

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