--- title: Graph Coloring description: Graph coloring is the assignment of labels to elements of a graph subject to certain constraints. Learners will understand how to color vertices, edges, or faces to avoid conflicts and solve scheduling and resource allocation problems. category: mathematics subcategory: graph-theory difficulty: beginner, intermediate, advanced url: /subject/graph-coloring --- # Graph Coloring Graph coloring is the assignment of labels to elements of a graph subject to certain constraints. Learners will understand how to color vertices, edges, or faces to avoid conflicts and solve scheduling and resource allocation problems. ## Available Resources 1 Books • 1 Courses • 3 Websites • 1 Papers ## Websites ### 1. Wikipedia Graph Coloring Overview, history, and algorithms **Difficulty:** Beginner | **Price:** Free **Link:** https://en.wikipedia.org/wiki/Graph_coloring ### 2. 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. **Difficulty:** Beginner | **Price:** Free **Link:** https://diestel-graph-theory.com/ **Tags:** graph-theory, textbook, discrete-mathematics, combinatorics, free-online ### 3. Wolfram MathWorld **Author:** Eric W. Weisstein 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. **Difficulty:** Intermediate | **Language:** English | **Price:** Free **Link:** https://mathworld.wolfram.com **Tags:** mathematics-reference, encyclopedia, abstract-algebra, number-theory, geometry ## Papers ### 1. An Update on the Four-Color Theorem **Author:** Robin Thomas 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. **Difficulty:** Intermediate | **Language:** English | **Price:** Free **Link:** https://thomas.math.gatech.edu/PAP/update.pdf **Tags:** four-color-theorem, graph-coloring, planar-graphs, discharging-method, reducible-configurations ## Books ### 1. Graph Coloring Problems Graph Coloring Problems - A book resource **Difficulty:** Intermediate | **Language:** English | **Price:** Paid **Link:** https://www.amazon.com/dp/0471028657?tag=edmonddante07-20 **Tags:** books, mathematics-statistics, graph-theory ## Courses ### 1. 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. **Difficulty:** Beginner | **Language:** English | **Duration:** 5 weeks, 3-5 hours/week | **Price:** Free **Link:** https://www.coursera.org/learn/graphs **Tags:** courses, mathematics-statistics, combinatorics --- *This content is part of Dantes.io - Your Treasure Map to Knowledge* *Curated by humans at Dantes.io. Personal study use welcome; republishing this curation requires permission (team@dantes.io).* View this page online: https://dantes.io/subject/graph-coloring