Wikipedia Graph Coloring
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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.
More resources on Graph Coloring
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.
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.
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.
Graph Coloring Problems
Research monograph cataloguing more than 200 open problems in graph coloring, each with its history, partial results, and references. Lets a reader with graduate-level graph theory locate the unsolved questions and the literature surrounding them.
Introduction to Graph Theory
We invite you to a fascinating journey into Graph Theory — an area which connects the elegance of painting and the rigor of mathematics; is simple, but not unsophisticated. Graph Theory gives us, both an easy way to pictorially represent many major mathematical results, and insights into the deep theories behind them. In this online course, among other intriguing applications, we will see how GPS systems find shortest routes, how engineers design integrated circuits, how biologists assemble genomes, why a political map can always be colored using a few colors. We will study Ramsey Theory which proves that in a large system, complete disorder is impossible! By the end of the course, we will implement an algorithm which finds an optimal assignment of students to schools. This algorithm, developed by David Gale and Lloyd S. Shapley, was later recognized by the conferral of Nobel Prize in Economics. As prerequisites we assume only basic math (e.g., we expect you to know what is a square or how to add fractions), basic programming in python (functions, loops, recursion), common sense and curiosity. Our intended audience are all people that work or plan to work in IT, starting from motivated high school students.