List questions from extremal-graph-theory

Published on 19 Dec 2021 - 8:19

321

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What is the smallest number of roads in a country?

Published on 30 Dec 2021 - 11:04

171

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Maximum number of edges in a balanced graph with n points, without small cycles (say, of length 2, 3, 4)

Published on 27 Mar 2026 - 0:05

813

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Erdos (1970) proof of Turan's Theorem - Applying induction on S

Published on 23 Jan 2022 - 1:29

326

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Using Mantel's theorem to prove a probabilistic inequality

Published on 31 Jan 2022 - 10:14

310

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Number of triangles in $K_n$ that don't share any edges

Published on 26 Mar 2026 - 19:03

221

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Lower bound for the largest number of triangles with a common edge

Published on 06 Feb 2022 - 11:06

137

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Inheriting $\epsilon$-regularity (Szemerédi graph regularity)

Published on 21 Feb 2022 - 9:56

183

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Lower bound of the Turan number $ex(n,C_4)$.

Published on 25 Mar 2026 - 13:57

275

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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

158

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Turan $K_4$-free problem of graphs with small independence number.

Published on 04 Mar 2022 - 11:30

315

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Maximal number of edges in $C_4$-free graph

Published on 09 Mar 2022 - 23:02

166

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Graphs which do not contain $C_4$ as an induced subgraph

Published on 11 Mar 2022 - 17:25

65

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Some basic properties of independence number of graph

Published on 12 Mar 2022 - 17:29

124

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Zarankiewicz's problem

Published on 18 Mar 2022 - 21:25

List Question

What are all the minimal prime extensions of the graph $P_3$?

What is the smallest number of roads in a country?

Maximum number of edges in a balanced graph with n points, without small cycles (say, of length 2, 3, 4)

Erdos (1970) proof of Turan's Theorem - Applying induction on S

Using Mantel's theorem to prove a probabilistic inequality

Number of triangles in $K_n$ that don't share any edges

Lower bound for the largest number of triangles with a common edge

Inheriting $\epsilon$-regularity (Szemerédi graph regularity)

Lower bound of the Turan number $ex(n,C_4)$.

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 $k$.

Turan $K_4$-free problem of graphs with small independence number.

Maximal number of edges in $C_4$-free graph

Graphs which do not contain $C_4$ as an induced subgraph

Some basic properties of independence number of graph

Zarankiewicz's problem

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