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The intent of the course is obtained by the student by attending the lessons. During the lessons everyone should feel free to pose questions at any time. To ensure the theory of lesson to be explained clearly and at a reasonable speed the blackboard will be used throughout the lessons. Further the exercises are of great help, and the answers are shown on the blackboard by the students.
The course consists of 3 lectures per week plus at least 6 tutorials. Since it is a two quarter course it consist of 42 lectures and at least 6 tutorials plus oral exam at the end of the course.
The course is placed as a candidate course. But it will be possible to follow the course at the end of a bachelor degree at the mathematic-economic study at Aarhus University. The course will fit very well for everyone interested in Operation Research or more general, for everyone interested in applied mathematics.
The topics, which make up of 90-100% of the course, are the following. The gap is devoted to suggestions coming from the students.
The course consists of 3 lectures per week plus at least 6 tutorials. Since it is a two quarter course it consist of 42 lectures and at least 6 tutorials plus an oral exam at the end of the course. The chapters are more or less of the same size, i.e. 6 lectures per chapter.
The topics are: introduction to Graph Theory (Chapter 1), special graphs (Spanning-, k-, and Cospanning-) trees, Circuits, cuts and cutsets (Chapter 2), Euler and Hamilton Graphs (chapter 3), oriented graphs (chapter 5), planarity of graphs (chapter 7) and connectivity and matchings in graphs (the beginning of chapter 8).
After the course the students should be familiar with all basic definitions in a graph (chapter 1 in the book used). And the students should know and be able to work with several operations on graphs such as the ring sum, the operation of adding/removing nodes and links from a graph. The notion of subgrahps should be a very familiar concept, such that a wide range of subgraphs with specific properties would cause no problem; subgraphs would appear as a very powerful tool in proofs and practical applications. The student should be able to work with graphs with some special properties such as the existence of an Euler Trail, a Hamilton circuit. But also be familiar with the notion of planarity of graphs and of course be able to make benefits from this property. The notion of edge- and node- k-connectedness is very important and the requirements are that the student can list benefits and drawbacks depending on various values of k. Concerning the theorems and proofs the requirements are that the student know the theorems and is able to reproduce their proofs. Depending on suggestions from the students some other topics can be added the course. Finally the students should be able to use graphs as a very powerful modeling tool. This should be the case as well for directed as undirected graphs.
Matematisk programmering.
Steen Friis Møller.
The course consists of lectures and in addition some tutorials. Both parts are held by the same teacher. There is no additional requirement to facilitate the course.
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The course is based on the book "Graphs: Theory and Applications" written by K. Thulasiraman and M. N. S. Swamy, Wileys, 1992. The book is used in both Graph Theory 1 and Graph Theory 2. Graph Theory 1 is based on the chapters 1,2,3,5,7 and 8 in the above mentioned book.
Swamy, M.N.S. and K. Thulasiraman: Graphs: Theory and Algorithms, John Wiley and Sons, 1992.
Eksamen: 2. kvarter. Reeksamen: Efter aftale med faglærer.
Institut for Matematiske Fag.
1.-15. maj 2007, Informationskontoret, Institut for Matematiske Fag.
Kurset evalueres efter 7-trinsskalaen med intern censur.
The exam is an individual oral exam without preparation time. The questions are not announced prior to the examination. But the list of literature on which the examination will be based is clear prior to the start of the course; some modifications are allowed, if the students have some specific wishes. The duration time of an examination is 30 minutes per student including drawing the question and the evaluation of the presentation. All this is every year cleared with the students. The set of marks used for evaluation is the 7-steps scale.
