SubjectsSubjects(version: 855)
Course, academic year 2019/2020
  
Graph Theory and Applications - AP413001
Title: Graph Theory and Applications
Guaranteed by: Department of Mathematics (413)
Actual: from 2019
Semester: both
Points: 0
E-Credits: 0
Examination process:
Hours per week, examination: 3/0 other [hours/week]
Capacity: winter:unknown / unknown (unknown)
summer:unknown / unknown (unknown)
Min. number of students: unlimited
Language: English
Teaching methods: full-time
Level:  
For type: doctoral
Note: course is intended for doctoral students only
can be fulfilled in the future
you can enroll for the course in winter and in summer semester
Guarantor: Turzík Daniel doc. RNDr. CSc.
Maxová Jana RNDr. Ph.D.
Interchangeability : D413012, P413001
Annotation -
Last update: Pátková Vlasta (08.06.2018)
The basic concepts of graph theory are introduced. Algorithmic solutions of engineering problems are discussed.
Aim of the course -
Last update: Pátková Vlasta (08.06.2018)

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.

Literature -
Last update: Pátková Vlasta (08.06.2018)

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.

Learning resources -
Last update: Pátková Vlasta (08.06.2018)

www.vscht.cz/mat/Ang/indexAng.html

Teaching methods -
Last update: Maxová Jana RNDr. Ph.D. (24.09.2018)

lectures, tutorials, individual work on the project

Syllabus -
Last update: Pátková Vlasta (08.06.2018)

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.

Entry requirements -
Last update: Borská Lucie RNDr. Ph.D. (16.09.2019)

Mathematics A, B

Registration requirements -
Last update: Borská Lucie RNDr. Ph.D. (16.09.2019)

none

Course completion requirements -
Last update: Pátková Vlasta (08.06.2018)

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.

 
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