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An introduction to graph theory

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arxiv 2308.04512 v3 pith:5KVKI3JB submitted 2023-08-02 math.HO math.CO

Darij Grinberg This is my paper
classification math.HOmath.CO
keywords graphintroductiontheoremtheoremstheorytreesanaloguesarborescences
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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).

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Cited by 4 Pith papers

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  1. An equality for balanced digraphs

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    The number of k-arc acyclic subdigraphs in which every vertex can reach a fixed root is independent of the root, for any balanced digraph.

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  4. An Introduction to Algebraic Combinatorics

    math.CO 2025-05 conditional novelty 2.0 of 10

    A proof-heavy, open-access graduate textbook on algebraic combinatorics, including a full proof of the Littlewood-Richardson rule.

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