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Heinold B. A Simple Introduction to Graph Theory

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Heinold B. A Simple Introduction to Graph Theory
Mount St. Mary’s University (Dept. of Math. and C.S.), 2019. — 134 p.
These are notes I wrote up for my graph theory class in 2016. 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 (200 in the whole, covering all chapters) at the end of notes (the majority of these exercises are ones I made up myself, but there are a few I adapted that were inspired by ones from other books, in particular "Introduction to Graph Theory", 2nd. ed. by Douglas B. West, and "Graph Theory: A Problem Oriented Approach" by Daniel A. Marcus, and "Introduction to Graph Theory" by Gary Chartrand and Ping Zhang. See any of those, especially West’s book, if you are looking for more challenging problems than the ones I have here).
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.
Last updated: July 9, 2019.
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