An introduction to graph theory

TL;DR

This graduate-level introduction to graph theory covers fundamental concepts, theorems, and applications, providing a comprehensive overview suitable for students and researchers new to the field.

Contribution

It offers a thorough, course-based overview of graph theory topics, including proofs and exercises, serving as an educational resource for advanced students.

Findings

Detailed coverage of key graph theory theorems

Introduction to network flows and matching theory

Extensive exercises for practice

Abstract

This is a graduate-level introduction to graph theory, corresponding to a quarter-long course. It covers simple graphs, multigraphs as well as their directed analogues, and more restrictive classes such as tournaments, trees and arborescences. Among the features discussed are Eulerian circuits, Hamiltonian cycles, spanning trees, the matrix-tree and BEST theorems, proper colorings, Turan's theorem, bipartite matching and the Menger and Gallai--Milgram theorems. The basics of network flows are introduced in order to prove Hall's marriage theorem. Around a hundred exercises are included (without solutions).