Course Description
MATH 6404: Applied [Combinatorics and] Graph Theory
CU Denver, Spring 2026
Instructor: Juan Carlos Martínez Mori
Syllabus
LaTex Macros
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Disclaimer:
These crowd-sourced notes are primarily intended to help you practice academic writing.
Reviewing them is optional; the lecture and your own notes remain the main source of course content.
They are compiled as is and have not been reviewed with the same rigor of a formal publication.
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Lecture 1: What is Combinatorics and Graph Theory?
[pdf]
[tex]
[Scribe: Carlos Martínez]
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Lecture 2: Graphs
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[tex]
[Scribe: Mark Johnson]
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Lecture 3: Combinatorial Arguments
[pdf]
[tex]
[Scribe: Simon Ruland]
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Lecture 4: Bijections and Cayley's Formula
[pdf]
[tex]
[Scribe: Jon Terry]
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Lecture 5: The Greedy Algorithm
[pdf]
[tex]
[Scribe: Lily Renneker]
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Lecture 6: Permutations, Sets, and Multisets
[pdf]
[tex]
[Scribe: Parsa S. Farahani]
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Lecture 7: Lattice Paths and the Catalan Numbers
[pdf]
[tex]
[Scribe: Baihan Liu]
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Lecture 8: Formal Power Series and Generating Functions
[pdf]
[tex]
[Scribe: Hanbyul (Han) Lee]
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Lecture 9: Recurrence Relations and the Fibonacci Numbers
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[tex]
[Scribe: Noura Allugmani]
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Lecture 10: The Fibonacci Numbers and the Chromatic Polynomial
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[tex]
[Scribe: Hunter Pearson]
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Lecture 11: The Principle of Inclusion-Exclusion and Graph Coloring
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[tex]
[Scribe: Simon Ruland]
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Lecture 12: Graph Coloring and Matchings
[pdf]
[tex]
[Scribe: Mark Johnson]
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Lecture 13: Maximum Matchings in Bipartite Graphs
[pdf]
[tex]
[Scribe: Noura Allugmani]
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Lecture 14: Minimum Vertex Covers in Bipartite Graphs
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[tex]
[Scribe: Hunter Pearson]
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Lecture 15: Graph Connectivty
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[tex]
[Scribe: Parsa S. Farahani]
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Lecture 16: Maximum Flows
[pdf]
[tex]
[Scribe: Baihan Liu]
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Lecture 17: The Max Flow - Min Cut Theorem
[pdf]
[tex]
[Scribe: Hanbyul (Han) Lee]
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Lecture 18: Applications of the Max Flow - Min Cut Theorem
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[tex]
[Scribe: Lily Renneker]
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Lecture 19: Planar Graphs
[pdf]
[tex]
[Scribe: Jon Terry]
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Lecture 20: Dual Graphs and Euler's Formula
[pdf]
[tex]
[Scribe: Noura Allugmani]
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Lecture 21: Planar Graph Coloring
[pdf]
[tex]
[Scribe: Mark Johnson]
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Lecture 22: Graph Laplacian
[pdf]
[tex]
[Scribe: Hanbyul (Han) Lee]
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Lecture 23: The Matrix-Tree Theorem
[pdf]
[tex]
[Scribe: Baihan Liu]
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Lecture 24: The Spectrum of the Graph Laplacian
[pdf]
[tex]
[Scribe: Simon Ruland]
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Lecture 25: Sperner's Lemma
[pdf pending]
[tex pending]
[Scribe: Jon Terry]
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Lecture 25: Lovász Local Lemma
[pdf pending]
[tex pending]
[Scribe: TBD]
Problem Sets
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Problem Set 1
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Problem Set 2
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Problem Set 3
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Problem Set 4
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Some Useful Links