An introduction to graph theory
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).
Keywords
Cite
@article{arxiv.2308.04512,
title = {An introduction to graph theory},
author = {Darij Grinberg},
journal= {arXiv preprint arXiv:2308.04512},
year = {2025}
}
Comments
454 pages, 300+ figures. Comments are welcome! The version at https://www.cip.ifi.lmu.de/~grinberg/t/22s/graphs.pdf will be updated more frequently. Some older materials are included as ancillary files, but can also be found at https://www.cip.ifi.lmu.de/~grinberg/t/17s . v3 adds subsections 4.6.3, 6.2.2 and 7.4 and a bunch of examples while also fixing minor mistakes