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The basic concepts of graph theory are introduced. Algorithmic solutions of engineering problems are discussed.
Last update: MAXOVAJ (08.06.2018)
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Students will acquire the basic concepts of graph theory. They will learn to analyze various engineering tasks and solve them using known graph algorithms. They will then learn how to recognize computationally hard tasks and gain insight into many of the problems solved by graph theory. Last update: MAXOVAJ (08.06.2018)
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The subject is finished by an oral exam. Before the exam is completed, 3 of the tasks assigned during the semester must be successfully solved. Last update: MAXOVAJ (07.06.2018)
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A: Matousek J., Nesetril J.: Invitation to Discrete Mathematics, Oxford University Press, USA, 2011. ISBN 978-0198570424
A: West D. B.: Introduction to Graph Theory. Pearson, 2001. ISBN 978-0130144003.
A: Diestel R.: Graph Theory (Graduate Texts in Mathematics). Springer, 2010. ISBN 978-3642142789.
A: Christofides N.: Graph Theory. An Algoritmic Approach. Academic Press Inc, 1975. ISBN 978-0121743505. Last update: MAXOVAJ (08.06.2018)
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lectures, tutorials, individual work on the project Last update: MAXOVAJ (24.09.2018)
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1. Basic concepts in graph theory. Representations of graphs.
2. Paths in graphs. The task of the shortest path.
3. Connected graphs, Components od connectivity, blocks of graphs.
4. Trees. Heap-sort.
5. Spanning tree. Greedy algorithm for minimal spanning tree.
6. System of distinct representatives. Matching in bipartite graphs.
7. Matching in general graphs.
8. Euler graphs. The Chinese postman problem.
9. Hamiltonian graphs. The travelling salesman problem.
10. Planar graphs and their characteristics.
11. Coloring. Coloring of Planar graphs.
12. Flows in networks.
13. Theory of complexity. P and NP problems. Good characteristics.
14. Examples of graph theory applications. Last update: MAXOVAJ (08.06.2018)
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www.vscht.cz/mat/Ang/indexAng.html Last update: MAXOVAJ (07.06.2018)
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none Last update: Mareš Jan (03.10.2018)
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