Question

$G$ contains two disjoint independent sets $A, B$ so that $|A| + |B| \geq 2\sum_{i=1}^n \frac{1}{d_{i}+1}$ where $d_{i}$ is degree of vertex $v_{i}$

score 183 · Answer 1 · 2021-12-05 22:27:17

183

Views

$G$ contains two disjoint independent sets $A, B$ so that $|A| + |B| \geq 2\sum_{i=1}^n \frac{1}{d_{i}+1}$ where $d_{i}$ is degree of vertex $v_{i}$

Published on 05 Dec 2021 - 22:27

score 41 · Answer 2 · 2022-01-09 18:10:18

41

Views

Intersection of Shifted Subsets of $\mathbb{Z}_n$

Published on 09 Jan 2022 - 18:10

score 157 · Answer 3 · 2022-02-15 20:27:34

157

Views

Show that there exists a $c > 0$ and a $n^$ such that for $n \geq n^$, every two coloring of $E(K_n)$ contains $cn^3$ monochromatic triangles.

Published on 15 Feb 2022 - 20:27

score 121 · Answer 4 · 2022-02-19 21:29:48

121

Views

Bounding the order of tournaments without transitive subtournaments of certain size.

Published on 19 Feb 2022 - 21:29

score 197 · Answer 5 · 2022-02-24 20:27:38

197

Views

Existence of an edge that is contained in at least two cycles

Published on 24 Feb 2022 - 20:27

score 275 · Answer 6 · 2022-03-02 10:32:54

275

Views

Let $k \geq 3 .$ Show that there exists a graph on $n$ vertices with $\Omega\left(n^{1+\frac{1}{k-1}}\right)$ many edges and no cycle of length $k$.

Published on 02 Mar 2022 - 10:32

score 127 · Answer 7 · 2022-03-26 11:11:01

127

Views

Existence of vertex in a triangle-free graph whose non-neighbours have at most $m(1-4m/n^2)$ edges.

Published on 26 Mar 2022 - 11:11

score 37 · Answer 8 · 2022-04-04 04:36:58

Are there Bernouilli random variables $X_1,...,X_k$ such that these variables are negatively correlated but $1-X_1,...,1-X_k$ are not?

score 35 · Answer 9 · 2022-04-23 09:42:59

35

Views

k-Cliques in the Random 3-Uniform Hypergraphs

Published on 23 Apr 2022 - 9:42

score 129 · Answer 10 · 2022-08-11 23:36:14

129

Views

Frieze and Karonski - Exercise 1.4.3 -- What is the significance of the $2$ here?

Published on 11 Aug 2022 - 23:36

score 175 · Answer 11 · 2022-09-10 03:59:51

175

Views

One question about the probabilistic method proof of the any large girth number and chromatic number on a graph.

Published on 10 Sep 2022 - 3:59

score 65 · Answer 12 · 2022-09-26 23:21:08

65

Views

Bound of the surface area of subset of the unit sphere in $\mathbb{R}^3$ with no pair of orthogonal points

Published on 26 Sep 2022 - 23:21

score 56 · Answer 13 · 2022-09-27 00:06:44

56

Views

Existence of a pair of isomorphic subgraphs in a given graph with large number of edges

Published on 27 Sep 2022 - 0:06

score 144 · Answer 14 · 2022-09-29 11:58:04

144

Views

Probability of a game never ending

Published on 29 Sep 2022 - 11:58

score 47 · Answer 15 · 2022-10-04 08:17:14

47

Views

Sort a group of distributions

Published on 04 Oct 2022 - 8:17

List Question

$G$ contains two disjoint independent sets $A, B$ so that $|A| + |B| \geq 2\sum_{i=1}^n \frac{1}{d_{i}+1}$ where $d_{i}$ is degree of vertex $v_{i}$

Intersection of Shifted Subsets of $\mathbb{Z}_n$

Show that there exists a $c > 0$ and a $n^$ such that for $n \geq n^$, every two coloring of $E(K_n)$ contains $cn^3$ monochromatic triangles.

Bounding the order of tournaments without transitive subtournaments of certain size.

Existence of an edge that is contained in at least two cycles

Let $k \geq 3 .$ Show that there exists a graph on $n$ vertices with $\Omega\left(n^{1+\frac{1}{k-1}}\right)$ many edges and no cycle of length $k$.

Existence of vertex in a triangle-free graph whose non-neighbours have at most $m(1-4m/n^2)$ edges.

Are there Bernouilli random variables $X_1,...,X_k$ such that these variables are negatively correlated but $1-X_1,...,1-X_k$ are not?

k-Cliques in the Random 3-Uniform Hypergraphs

Frieze and Karonski - Exercise 1.4.3 -- What is the significance of the $2$ here?

One question about the probabilistic method proof of the any large girth number and chromatic number on a graph.

Bound of the surface area of subset of the unit sphere in $\mathbb{R}^3$ with no pair of orthogonal points

Existence of a pair of isomorphic subgraphs in a given graph with large number of edges

Probability of a game never ending

Sort a group of distributions

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