Heinold B. A Simple Introduction to Graph Theory 2024

Textbook in PDF format

These are notes I wrote up for my graph theory class. They contain most of the topics typically found in a graph theory course. There are proofs of a lot of the results, but not of everything. I’ve designed these notes for students that don’t have a lot of previous experience in math, so I spend some time explaining certain things in more detail than is typical. My writing style is also pretty informal. There are a number of exercises at the end.
Preface.
Basics.
Proofs, Constructions, Algorithms, and Applications.
Bipartite Graphs and Trees.
Eulerian and Hamiltonian graphs.
Coloring.
Planar Graphs.
Matchings and Covers.
Digraphs.
Connectivity.
Epilogue and Bibliography.
Exercises.
Index