Graph Theory Final Project Resources

Graph Theory Final Project Resources

Turan's Theorem and other extremal graph theory
The Matrix-Tree Theorem
Min-max theorems
Graph labeling, including graceful labeling, magic labeling, etc.

A Dynamic Survey of Graph Labeling, Joseph Gallian

Network flows (Algorithms) -- Megan
Perfect graphs and chordal graphs
Crossing number -- Ryan

Pearls in Graph Theory section 9.1

Graph Connections section 11.4

Graphs on surfaces of higher genus (Topology)

Pearls in Graph Theory section 10.3

Graph Connections chapter 11

Snarks -- Marisa
Matroids (Linear Algebra)

Graph Connections chapter 7

Ramsey Theory

Small Ramsey Numbers, Stanislaw P. Radziszowski

List Coloring and Choosability
The Empire Problem -- Shijun

Joan Hutchinson, Coloring ordinary maps, maps of empires, and maps on the moon

Random Graphs (Probability)
Eigenvalues of graphs (Linear Algebra)
Moore graphs -- Wade

Moore graphs and beyond: A survey of the degree/diameter problem, Miller and Suran

Ordered sets -- Kali, Jared

Combinatorics and Partially Ordered Sets: Dimension Theory, William T. Trotter, chapter 1

Geometric graphs and intersection graphs -- Alvaro

Graph Connections, chapter 10

Tolerance graphs -- Brett

Graph pebbling

Glenn Hurlbert, A survey of graph pebbling

Glenn Hurlbert, Recent progress in graph pebbling

Domination in graphs -- Matt

Domination in graphs: a survey, Michael Henning

Dominations in graphs: a brief overview, Teresa Haynes

Graph automorphisms (Abstract Algebra) -- Malcolm

Graph Connections, chapter 9

Bandwidth -- Dan

The bandwidth problem for graphs and matrices, a survey, Chinn, Chvatalova, Dewdney, and Gibbs

Hypergraphs -- Leo

Hypergraphs : combinatorics of finite sets, Claude Berge, chapter 1

Phylogenetic trees (Biology)

Identifying phylogenetic trees, Bordewich, Huber, Semple

Phylogenetics, Charles Semple and Mike Steel, sections 1.3, 1.4, 2.1, 2.2, 2.3, 4.1, 4.2

Molecular and intrinsically linked graphs (Topology, Chemistry)