This web content provides a graduate-level introduction to graph theory, equivalent to a quarter-long course. It encompasses various types of graphs, including simple graphs, multigraphs, and directed analogues. The content explores more specific classes such as tournaments, trees, and arborescences. Notable features discussed include Eulerian circuits, Hamiltonian cycles, spanning trees, matrix-tree and BEST theorems, proper colorings, Turan’s theorem, bipartite matching, and the Menger and Gallai-Milgram theorems. The author introduces the basics of network flows to establish the proof for Hall’s marriage theorem. The content concludes with approximately one hundred exercises for further practice. No solutions to the exercises are provided.

https://arxiv.org/abs/2308.04512