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Resources on Graph theory and Dynamic programming

Books

Digraphs Theory, Algorithms, and Applications, Bang-Jensen and Gutin, 2007

Dynamic Programming, Richard Bellman, Princeton, 1957, Sixth Print 1972

The Theory of Dynamic Programming, Richard Bellman, 1954

Dynamic Programming and Optimal Control, Vol. I, Third Edition, Dimitri P. Bertsekas, 2005

Dynamic Programming and Principles of Optimality, Moshe Sniedovich, 1978

The Elements of Differentiable Programming, Mathieu Blondel, Vincent Roulet, Google DeepMind, 2024

Articles

Network Flow

Flows in Networks, L.R. Ford and D.R. Fulkerson, 1962

Optimal matching

College Admissions and the Stability of Marriage, D. Gale and L.S. Shapley, 1962

The Assignment Game I: The Core, L. Shapley and M. Shubik, 1971, Rand Corp

On-Line and First Fit Colorings of Graphs, A. Gyafras, J. Lehel, 1988

An Optimal Algorithm for On-line Bipartite Matching, Richard Karp, Umesh vazirani et al, 1990

The Assignment Game: The Reduced Game, Guillermo Owen, 1992

AdWords and Generlized Online Matching, A. Mehta et al, 2007

Online Matching and Ad Allocation, A. Mehta, 2013

Markov Chains

A Tutorial on the Spectral Theory of Markov Chains, E. Seabrook et al, 2022

Spectral Graph Theory

Spectra of graphs, Andries E. Brouwer, Willem H. Haemers, 2011

Study of Eigenspaces in Graphs, D. Cvetkovic et al, 1993

Eigenvalues of graphs, Laszlo Lovasz, 2007

Eigenvalues and structures of graphs, SK. Butler, PhD Thesis, UC San Diego, 2008

On Simply Structured Bases of Graph Eigenspaces, Torsten Sander, 2008

Are Almost All Graphs Cospectral?, Chris Godsil, 2007

Vertex-Frequency Analysis on Graphs, D. Shuman et al, 2013

Reconstructing Undirected Graphs from Eigenspaces, Yohann De Castro et al, 2017

An Introduction to the Theory of Graph Spectra, MATH-495/595 Iowa State University, SK Butler, 2017, youtube video lectures

Expander Graphs

A Note on High Dimensional Expanders

High Dimensional Expanders, A. Lubotsky, 2017

High Dimensional Expanders, Ori Parzanchevski, PhD Thesis, Princeton U, 2013

Expander Codes, Michael Spiser, Daniel Spielman, MIT, 1996

Percolation Theory

Percolation: A Close-Up View Reveals the ‘Melting’ Point of an Infinite Graph, Quanta Magazine, 2023

Percolation, Geoffrey Grimmett, 1997

The Critical Percolation Probability is local, Philip Easo, Tom Hutchcroft, 2023

Percolation Theory for Mathematicians - all chapters here...

medium

The Essential Guide to Graph Theory: From an 18th Century Riddle to Artificial Intelligence, Sydney Nye, May, 2024

youtube lectures

Spectral Graph Theory

An Introduction to the Theory of Graph Spectra, MATH-495/595 Iowa State University, SK Butler, 2017, youtube video lectures