graph theory

This course is devoted to Graph theory.

A graph is a mathematical structure modeling a pairwise relation between objects. A graph is thus a collection of points (aka, vertices or nodes) with edges (arrows) drawn between them. The mathematician Leonhard Euler was the first to introduce Graph theory, when he presented his solution to the problem of the Königsberg bridge, in 1736. Since then, graph theory has increasingly attracted the interest of researchers in mathematics and in other scientific areas, due to its enormous applications in computer science, biology, chemistry, social sciences, amongst others.  In this course we will give an overview of the fundaments of graph theory, followed by the topics of trees and forests. We then study Eulerian paths and Hamiltonian circuits. The Theorems of Maximum Flow - Minimum Cut and of Menger are referred for Networks, and Kuratowski's Theorem and The Four-Color Conjecture for Planar Graphs. We end the course with the analysis of the complexity of some well-known algorithms.

Enjoy the course!