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Lecture 6: Graph Theory and Coloring (MIT 6.042J Mathematics for Computer Science)

by Tom Leighton · MIT OpenCourseWare

Tom Leighton's MIT lecture introducing graphs and vertex coloring through scheduling problems such as exam timetabling, covering chromatic number, simple coloring bounds, and the greedy coloring argument, with free course notes and problem sets alongside.

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Wolfram MathWorld

MathWorld is an online mathematics encyclopedia from Wolfram Research offering detailed, browsable articles on topics across the math spectrum, including algebra, geometry, calculus, and number theory. Each entry includes definitions, theorems, formulas, diagrams, worked examples, and links to further reading.

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Wikipedia Graph Coloring

Encyclopedia article covering vertex, edge, and total coloring, the chromatic number and polynomial, the four color theorem, and standard algorithms with their complexity. Gives a reader the vocabulary and landmark results needed before opening a graph theory textbook.

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Diestel Graph Theory

Official site for Reinhard Diestel's Springer graduate text, where the main text is readable free online and paid eBook editions add the full apparatus. It covers matching, connectivity, planarity, colouring, flows, extremal theory, and minors.

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Graph Colouring and the Probabilistic Method

The definitive graduate/research text on modern colouring results via probability. Research monograph developing probabilistic tools, including the Lovász Local Lemma, Talagrand's inequality and the semi-random method, and applying them to colouring results such as Kahn's list edge colouring work, Johansson's theorem for triangle-free graphs, and total colouring bounds.

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Guide to Graph Colouring: Algorithms and Applications (2nd edition)

Algorithmic treatment of graph colouring covering greedy, DSatur, RLF, backtracking, tabu search and other metaheuristics, with comparisons on benchmark graphs and applications to timetabling, sports scheduling and seating plans. Supported by downloadable C++ source code.

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An Update on the Four-Color Theorem

Survey by a co-author of the 1997 simplified proof. Traces the history of map coloring, explains why the problem is really about planar graphs, and walks through discharging, reducibility, the 633 configurations, and the resulting quadratic-time coloring algorithm.

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