SubjectsSubjects(version: 954)
Course, academic year 2019/2020
  
Graph Theory and Applications - AP413001
Title: Graph Theory and Applications
Guaranteed by: Department of Mathematics (413)
Faculty: Faculty of Chemical Engineering
Actual: from 2019 to 2020
Semester: both
Points: 0
E-Credits: 0
Examination process:
Hours per week, examination: 3/0, other [HT]
Capacity: winter:unknown / unknown (unknown)
summer:unknown / unknown (unknown)
Min. number of students: unlimited
State of the course: taught
Language: English
Teaching methods: full-time
Teaching methods: full-time
Level:  
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 : P413001
Examination dates   Schedule   
Annotation -
The basic concepts of graph theory are introduced. Algorithmic solutions of engineering problems are discussed.
Last update: Pátková Vlasta (08.06.2018)
Aim of the course -

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: Pátková Vlasta (08.06.2018)
Literature -

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: Pátková Vlasta (08.06.2018)
Learning resources -

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

Last update: Pátková Vlasta (08.06.2018)
Teaching methods -

lectures, tutorials, individual work on the project

Last update: MAXOVAJ (24.09.2018)
Syllabus -

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: Pátková Vlasta (08.06.2018)
Entry requirements -

Mathematics A, B

Last update: Borská Lucie (16.09.2019)
Registration requirements -

none

Last update: Borská Lucie (16.09.2019)
Course completion requirements -

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: Pátková Vlasta (08.06.2018)
 
VŠCHT Praha