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Preprint (Author's original)arXiv.org - Non-exclusive license to distribute, Open
Preprint
An introduction to graph theory
arXiv.org
02 Aug 2023
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).
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Details
- Title
- An introduction to graph theory
- Creators
- Darij Grinberg
- Publication Details
- arXiv.org
- Resource Type
- Preprint
- Language
- English
- Academic Unit
- Mathematics
- Other Identifier
- 991021862240904721