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 The Bridges of Königsberg - Isaac Reed This problem inspired the great Swiss mathematician Leonard Euler to create graph theory, which led to the development of topology. more>> The Four Colour Theorem - MacTutor Math History Archives Linked essay describing work on the theorem from its posing in 1852 through its solution in 1976, with two other web sites and 9 references (books/articles). more>> Graph Theory - Dave Rusin; The Mathematical Atlas A short article designed to provide an introduction to graph theory. A graph is a set V of vertices and a set E of edges - pairs of elements of V. This simple definition makes Graph Theory the appropriate language for discussing (binary) relations on sets. Among the topics of interest are topological properties such as connectivity and planarity (can the graph be drawn in the plane?); counting problems (how many graphs of a certain type?); coloring problems (recognizing bipartite graphs, the Four-Color Theorem); paths, cycles, and distances in graphs (can one cross the Königsberg bridges exactly once each?). Many graph-theoretic topics are the object of complexity studies in computation (e.g. the Travelling Salesman problem, sorting algorithms, the graph-isomorphism problem). The theory also extends to directed, labelled, or multiply-connected graphs. History; applications and related fields and subfields; textbooks, reference works, and tutorials; software and tables; other web sites with this focus. more>> Graph Theory Tutorials - Chris K. Caldwell A series of short interactive tutorials introducing the basic concepts of graph theory, designed with the needs of future high school teachers in mind and currently being used in math courses at the University of Tennessee at Martin. An Introduction to Graph Theory tutorial uses three motivating problems to introduce the definition of graph along with terms like vertex, arc, degree, and planar. Includes a glossary and a partially annotated bibliography of graph theory terms and resources. Euler Circuits and Paths; Coloring Problems (Maps). more>> Perfect Problems - Vasek Chvátal Unsolved problems on perfect graphs, a collection for people with at least a basic knowledge of the subject. Contents include: Perfection of special classes of Berge graphs; Recognition of special classes of Berge graphs; Decompositions of perfect graphs; Minimal imperfect graphs, partitionable graphs, and monsters; Parity problems; The P4-structure; Quantitative variations on the Strong Perfect Graph Conjecture; Intersection graphs; The Markosyan manoeuvre; Appendix: Odds and ends. With a bibliography, and home pages of people interested in perfect graphs. more>>
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