Graph Theory IITechnical University of DenmarkGeneral course objectives: The course includes a number of classical results such as the theorems of Tutte, Ramsey, Turan, Kuratowski, Brooks, Dirac, Smith, and Vizing, respectively, and also the Jordan Curve Theorem. The course also includes more recent themes, for example listcolorings. Learning objectives: A student who has met the objectives of the course will be able to:
Contents: 1.Generating functions, the Catalan numbers. 2.Tutte’s 1factor theorem. Petersen’s theorem. 3.The theorems of Ramsey og Turan. 4.The Jordan Curve Theorem. 5.Kuratowski’s theorem on planar graphs. 6.Hamilton cycles. Dirac’s theorem and the Grinberg criterion. 7.The number of hamilton cycles (Smith’s theorem) , chromatic number and maximum degree (Brooks’ theorem). 8.Vizing’s theorem on chromatic index. 9.Listcoloring 10.Chromatic polynomial. 11.Directed graphs. 12.Graphs of large chromatic number and large girth. 
