Question

Let $G$ be a graph on $n$ vertices and without any cycle of length $4$. Show that $G$ has at most $\frac n2(\sqrt n+1)$ edges.

score 522 · Answer 1 · 2021-09-11 22:18:10

522

Views

Let $G$ be a graph on $n$ vertices and without any cycle of length $4$. Show that $G$ has at most $\frac n2(\sqrt n+1)$ edges.

Published on 11 Sep 2021 - 22:18

score 56 · Answer 2 · 2026-03-25 09:25:35

56

Views

On $F_k$-free extermal graphs

Published on 25 Mar 2026 - 9:25

score 295 · Answer 3 · 2021-09-25 21:37:12

295

Views

Number of seats required in the generalised Wolf-Goat-Cabbage riddle

Published on 25 Sep 2021 - 21:37

score 138 · Answer 4 · 2021-09-25 22:16:30

138

Views

Inequality between number of triangles and number of edges in a graph

Published on 25 Sep 2021 - 22:16

score 34 · Answer 5 · 2026-03-25 09:23:54

34

Views

"Big-$O$ version" of graph counting lemma?

Published on 25 Mar 2026 - 9:23

score 163 · Answer 6 · 2021-10-06 03:59:45

163

Views

Ramsey-Turán density function is well defined.

Published on 06 Oct 2021 - 3:59

score 77 · Answer 7 · 2021-10-09 13:01:57

77

Views

Existence of a path of length $n/2$ in every bipartite graph with $d(A,B)=1/2$.

Published on 09 Oct 2021 - 13:01

score 82 · Answer 8 · 2021-10-24 02:41:50

82

Views

If the degree of every vertex in a graph on $n$ vertices is greater than $(1+ \sqrt{4n-3})/2$, then the graph contains a cycle of length $4$

Published on 24 Oct 2021 - 2:41

score 641 · Answer 9 · 2021-10-28 00:10:15

641

Views

How to prove the sum of squares degrees $d^2_{1}+d^2_{2}+\cdots+d^2_{95}\le 300000$ in a graph

Published on 28 Oct 2021 - 0:10

score 140 · Answer 10 · 2021-11-17 16:08:57

140

Views

What is $\operatorname{ex}(n, K_{2,3})$?

Published on 17 Nov 2021 - 16:08

score 92 · Answer 11 · 2021-11-22 13:23:11

92

Views

Question 12.2.1 of Bondy's Graph Theory

Published on 22 Nov 2021 - 13:23

score 59 · Answer 12 · 2021-11-29 23:26:21

59

Views

Upper bound for set of vertices intersecting all triangles in a graph

Published on 29 Nov 2021 - 23:26

score 132 · Answer 13 · 2021-12-07 17:44:04

132

Views

Extremal combinatorics

Published on 07 Dec 2021 - 17:44

score 262 · Answer 14 · 2021-12-16 15:59:19

262

Views

What's the minimum number of people required?

Published on 16 Dec 2021 - 15:59

score 59 · Answer 15 · 2021-12-18 03:25:26

59

Views

Minimum number of edges for a specific type of graph.

Published on 18 Dec 2021 - 3:25

List Question

Let $G$ be a graph on $n$ vertices and without any cycle of length $4$. Show that $G$ has at most $\frac n2(\sqrt n+1)$ edges.

On $F_k$-free extermal graphs

Number of seats required in the generalised Wolf-Goat-Cabbage riddle

Inequality between number of triangles and number of edges in a graph

"Big-$O$ version" of graph counting lemma?

Ramsey-Turán density function is well defined.

Existence of a path of length $n/2$ in every bipartite graph with $d(A,B)=1/2$.

If the degree of every vertex in a graph on $n$ vertices is greater than $(1+ \sqrt{4n-3})/2$, then the graph contains a cycle of length $4$

How to prove the sum of squares degrees $d^2_{1}+d^2_{2}+\cdots+d^2_{95}\le 300000$ in a graph

What is $\operatorname{ex}(n, K_{2,3})$?

Question 12.2.1 of Bondy's Graph Theory

Upper bound for set of vertices intersecting all triangles in a graph

Extremal combinatorics

What's the minimum number of people required?

Minimum number of edges for a specific type of graph.

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