Mantel's Theorem: Extremal Graph Theory Primer, and Intro To Turan's Theorem

preview_player
Показать описание
In this video we discuss the problem of finding a tight upper bound on the number of edges a graph on n vertices can have if it is also known that the graph has no 3-cycle in it. This is known as Mantel's Theorem and it is a special case of Turan's Theorem which generalizes this problem from a 3-cycle (a complete graph on 3 vertices) to complete graphs on arbitrary numbers of vertices.

#TuranGraph #MantelsTheorem #GraphTheory

CHECK OUT OTHER TYPES OF VIDEOS:

================================

GET MY BOOK ON AMAZON!!
========================

"Number Theory Towards RSA Cryptography in 10 Undergraduate Lectures"

CHECK ME OUT ON THE INTERNET!!
==============================

Twitter: @ProfOmarMath
Instagram: profomarmath

And of course, subscribe to my channel!
  1. Mohamed Omar
  2. turans theorem pdf
  3. turan graph number of edges
  4. erdos stone theorem
  5. extremal graph theory
  6. mantel graph theory
Рекомендации по теме
Mantel's Theorem: Extremal 0:18:04

Mantel's Theorem: Extremal Graph Theory Primer, and Intro To Turan's Theorem

Mantel's Theorem. MATH 0:18:00

Mantel's Theorem. MATH 492/529 Extremal Combinatorics, University of Victoria.

Mantel's Theorem - 0:05:12

Mantel's Theorem - Introduction to Graph Theory

Extremal Graph theory: 0:14:52

Extremal Graph theory: Mantel's theorem proof

Graph Theory lecture#10 0:53:04

Graph Theory lecture#10 Extremal Problems Mantel's Theorem

Mantel's Theorem 0:07:33

Mantel's Theorem

2. Forbidding a 1:12:41

2. Forbidding a subgraph I: Mantel's theorem and Turán's theorem

extremal graph theory: 0:13:06

extremal graph theory: prove Kovari-Sos-Turan theorem

Extremal Graph Theory 0:54:38

Extremal Graph Theory and the Problem of Zarankiewicz: Part 1

Lecture21 Extremal Graph 1:03:20

Lecture21 Extremal Graph Theory (2/3)

Extremal graph theory: 0:15:08

Extremal graph theory: prove Turan's theorem

MAT0067 Graph Theory 0:55:10

MAT0067 Graph Theory Honours Lecture 11 Extremal Graphs

Kővári–Sós–Turán Theorem. MATH 0:20:31

Kővári–Sós–Turán Theorem. MATH 492/529 Extremal Combinatorics, University of Victoria.

Turán's Theorem. MATH 0:34:27

Turán's Theorem. MATH 492/529 Extremal Combinatorics, University of Victoria.

2021 Graph theory 1:07:32

2021 Graph theory Lecture 22, Extremal graph theory (1)

Graph Theory 9-1: 0:29:58

Graph Theory 9-1: Turan's Theorem

Part 2: Turán's 0:20:05

Part 2: Turán's theorem

Extremal Graph Theory 1:02:58

Extremal Graph Theory and the Problem of Zarankiewicz: Part 2

Erdős–Stone Theorem. MATH 1:19:35

Erdős–Stone Theorem. MATH 492/529 Extremal Combinatorics, University of Victoria.

Extremal Combinatorics Lecture 0:55:38

Extremal Combinatorics Lecture 12: Mantel's Theorem

Wolf Prize Laureate 1:13:37

Wolf Prize Laureate Laszlo Lovasz on 'Which Graphs Are Extremal?'

2016-11-01 Michael Tait 0:48:57

2016-11-01 Michael Tait - Four conjectures in spectral extremal graph theory

Stability for Turán's 0:33:04

Stability for Turán's Theorem. MATH 492/529 Extremal Combinatorics, University of Victoria.

Andrey Kupavskii: The 1:00:55

Andrey Kupavskii: The extremal number of surfaces

Комментарии
Автор

Excellent explanation, thank you Professor.

valeriereid
Автор

The inductive argument is more natural. The other approach is less natural, but it's not difficult to deduce once you think of adding the inequalities of the lemma, because you then know that you need to give rise to a larger power of E(G) to the right-hand side, which is usually done with C-S. Nice video!

Stelios
Автор

Very nice! Since we know when the maximum is attained, I wonder if we could prove that any triangle-free graph has less edges than the corresponding bi-partite special graphs mentioned in the beginning of the presentation.

yanmich