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Graph Theory II


Technical University of Denmark


General 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 list-colorings.

Learning objectives:
A student who has met the objectives of the course will be able to:
  • Apply generating functions.
  • Apply counting technique illustrated by Ramsey's theorem.
  • Apply the foundation for planar graphs: The Jordan Curve Theorem.
  • Apply the Kuratowski Planarity Criterion.
  • Understand and apply the classical theorems by Turan, Brooks, Dirac, Smith, Vizing, Roy-Gallai, Camion and Robbins.
  • Apply list-color method.
  • Apply algebraic methods illustrated by the chromatic polynomial.
  • Understand the probabilistic method illustrated by graphs with large chromatic number and large girth.

Contents:
1.Generating functions, the Catalan numbers. 2.Tutte’s 1-factor 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.List-coloring 10.Chromatic polynomial. 11.Directed graphs. 12.Graphs of large chromatic number and large girth.

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Course organizer
Carsten
Place/Venue
Anker Engelunds Vej 1
City
2800 Kgs. Lyngby
Country
Denmark
Workload
5
Link
http://kurser.dtu.dk/course/01527