Notes on Graph Product Structure Theory

Notes on graph theory

2. Introduction 3 2.1. Notations and conventions . . . . . . . . . . . . . . . . . . . . . . . . 4 2.2. Simple graphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.3. Drawing graphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.4. A first fact: The Ramsey number R (3, 3) = 6 . . . . . . . . . . . . . . 11 2.5. Degrees . . . . . . . . . . . . . . . . . ....

Lecture Notes on GRAPH THEORY

Lecture Notes on Graph Theory

A graph G = (V,E) consists of two finite sets V and E. The elements of V are called the vertices and the elements of E the edges of G. Each edge is a pair of vertices. For instance, V = {1, 2, 3, 4, 5} and E = {{1, 2}, {2, 3}, {3, 4}, {4, 5}}. Graphs have natural visual representations in which each vertex is represented by a point and each edge by a line connecting two points. b b b b b 1 2 3 4 5

Notes on Extremal Graph Theory

What you see below are notes related to a course that I have given several times in Extremal Graph Theory. I guarantee no accuracy with respect to these notes and I certainly do not guarantee completeness or proper attribution. This is an early draft and, with any luck and copious funding, some of this can be made into a publishable work and some will just remain as notes. Please do not distrib...

Graph Theory Notes ∗

A graph G = (V,E) consists of two sets V and E. The elements of V are called the vertices and the elements of E the edges of G. Each edge is a pair of vertices. For instance, the sets V = {1, 2, 3, 4, 5} and E = {{1, 2}, {2, 3}, {3, 4}, {4, 5}} define a graph with 5 vertices and 4 edges. Graphs have natural visual representations in which each vertex is represented by a point and each edge by a...