Gurantor department | Department of Applied Mathematics | Credits | 6 |

Subject guarantor | doc. Mgr. Petr Kovář, Ph.D. | Subject version guarantor | doc. Mgr. Petr Kovář, Ph.D. |

Study level | undergraduate or graduate | Requirement | Optional |

Year | Semester | summer | |

Study language | Czech | ||

Year of introduction | 2010/2011 | Year of cancellation | |

Intended for the faculties | FEI | Intended for study types | Follow-up Master |

Instruction secured by | |||
---|---|---|---|

Login | Name | Tuitor | Teacher giving lectures |

KOV16 | doc. Mgr. Petr Kovář, Ph.D. |

Extent of instruction for forms of study | ||
---|---|---|

Form of study | Way of compl. | Extent |

Full-time | Credit and Examination | 2+2 |

Part-time | Credit and Examination | 10+10 |

Each student is supposed to
- analyze real life problems
- express them as a graph theory problem
- solve the problem using graph theory methods
- give an interpretation of the theoretical results in the terms of the original problems
At the same time he should decide what are the limits of an ideal theoretical solution in contrast to the real situation.

Lectures

Individual consultations

Tutorials

Project work

The course covers both basic and advanced topics of Graph Theory, often overlapping with other branches of mathematics (algebra, combinatorics).
A mandatory part of the course is one or sometimes two projects focused on real life problems that are solved using methods of graph theory.

J. Matoušek, J. Nešetřil, Chapters in Discrete Mathematics, Karolinum Praha (2010).

D. B. West, Introduction to graph theory, Prentice-Hall, Upper Saddle River NJ, (2019), ISBN 9780131437371.

During the semester each student prepares one or two projects.
Topic of each project is chosen among topics presented in the lecture.
The sumbission date and all assignments are available on the instructor webpage or in the university electronic information system.
(Each student has to register for a topic.)
For a pass it is necessary to have at least one project graded for at least 10 points.

There are no other requirements.

Subject has no prerequisities.

Subject has no co-requisities.

Lectures and discussions:
1) Graphs, simple graphs. Incidence matrix and adjacency matrix. Subgraphs. Degree of a vertex.
2) Paths and cycles.
3) Trees, bridges and cuts.
4) Graph isomorphisms.
5) Connectivity and blocks. Cut sets.
6) Matching and covers in general and bipartite graphs. Perfect matchings.
7) Edge colorings. Chromatic index, Vizing's Theorem.
8) Vertex colorings, Chromatic number, Brook's Theorem.
9) Planar graphs. Dual graphs, Euler's formula for connected planar graphs, Kuratowski's Theorem. Four Color Theorem.
10) Non-planar graph, measures of non-planarity.
11) Eulerian and Hamiltonian graphs.
12) Oriented graphs. Oriented paths and cycles.
13) Tournaments and graph models
14) Further topics: flows in networks, cuts.

Task name | Type of task | Max. number of points
(act. for subtasks) | Min. number of points | Max. počet pokusů |
---|---|---|---|---|

Exercises evaluation and Examination | Credit and Examination | 100 (100) | 51 | |

Exercises evaluation | Credit | 20 (20) | 10 | |

Project | Project | 20 | 10 | |

Examination | Examination | 80 (80) | 41 | 3 |

Written exam | Written examination | 60 | 30 | |

Theoretical part | Oral examination | 20 | 5 |

Show history

Conditions for subject completion and attendance at the exercises within ISP:

Show history

Academic year | Programme | Field of study | Spec. | Zaměření | Form | Study language | Tut. centre | Year | W | S | Type of duty | |
---|---|---|---|---|---|---|---|---|---|---|---|---|

2022/2023 | (N0541A170007) Computational and Applied Mathematics | (S01) Applied Mathematics | NMS | K | Czech | Ostrava | 2 | Compulsory | study plan | |||

2022/2023 | (N0541A170007) Computational and Applied Mathematics | (S01) Applied Mathematics | NMS | P | Czech | Ostrava | 2 | Compulsory | study plan | |||

2021/2022 | (N0541A170007) Computational and Applied Mathematics | (S01) Applied Mathematics | P | Czech | Ostrava | Choice-compulsory type B | study plan | |||||

2021/2022 | (N0541A170007) Computational and Applied Mathematics | (S01) Applied Mathematics | K | Czech | Ostrava | Choice-compulsory type B | study plan | |||||

2020/2021 | (N2647) Information and Communication Technology | (1103T031) Computational Mathematics | P | Czech | Ostrava | Optional | study plan | |||||

2020/2021 | (N2647) Information and Communication Technology | (1103T031) Computational Mathematics | K | Czech | Ostrava | Optional | study plan | |||||

2020/2021 | (N0541A170007) Computational and Applied Mathematics | (S01) Applied Mathematics | K | Czech | Ostrava | Choice-compulsory type B | study plan | |||||

2020/2021 | (N0541A170007) Computational and Applied Mathematics | (S01) Applied Mathematics | P | Czech | Ostrava | Choice-compulsory type B | study plan | |||||

2019/2020 | (N2647) Information and Communication Technology | (1103T031) Computational Mathematics | P | Czech | Ostrava | Optional | study plan | |||||

2019/2020 | (N2647) Information and Communication Technology | (1103T031) Computational Mathematics | K | Czech | Ostrava | Optional | study plan | |||||

2019/2020 | (N0541A170007) Computational and Applied Mathematics | (S01) Applied Mathematics | P | Czech | Ostrava | Choice-compulsory type B | study plan | |||||

2019/2020 | (N0541A170007) Computational and Applied Mathematics | (S01) Applied Mathematics | K | Czech | Ostrava | Choice-compulsory type B | study plan | |||||

2018/2019 | (N2647) Information and Communication Technology | (1103T031) Computational Mathematics | P | Czech | Ostrava | Optional | study plan | |||||

2018/2019 | (N2647) Information and Communication Technology | (1103T031) Computational Mathematics | K | Czech | Ostrava | Optional | study plan | |||||

2017/2018 | (N2647) Information and Communication Technology | (1103T031) Computational Mathematics | P | Czech | Ostrava | Optional | study plan | |||||

2017/2018 | (N2647) Information and Communication Technology | (1103T031) Computational Mathematics | K | Czech | Ostrava | Optional | study plan | |||||

2016/2017 | (N2647) Information and Communication Technology | (1103T031) Computational Mathematics | P | Czech | Ostrava | Optional | study plan | |||||

2016/2017 | (N2647) Information and Communication Technology | (1103T031) Computational Mathematics | K | Czech | Ostrava | Optional | study plan | |||||

2015/2016 | (N2647) Information and Communication Technology | (1103T031) Computational Mathematics | P | Czech | Ostrava | Optional | study plan | |||||

2015/2016 | (N2647) Information and Communication Technology | (1103T031) Computational Mathematics | K | Czech | Ostrava | Optional | study plan | |||||

2014/2015 | (N2647) Information and Communication Technology | (1103T031) Computational Mathematics | P | Czech | Ostrava | Optional | study plan | |||||

2014/2015 | (N2647) Information and Communication Technology | (1103T031) Computational Mathematics | K | Czech | Ostrava | Optional | study plan | |||||

2013/2014 | (N2647) Information and Communication Technology | (1103T031) Computational Mathematics | P | Czech | Ostrava | Optional | study plan | |||||

2013/2014 | (N2647) Information and Communication Technology | (1103T031) Computational Mathematics | K | Czech | Ostrava | Optional | study plan | |||||

2012/2013 | (N2647) Information and Communication Technology | (1103T031) Computational Mathematics | P | Czech | Ostrava | Optional | study plan | |||||

2012/2013 | (N2647) Information and Communication Technology | (1103T031) Computational Mathematics | K | Czech | Ostrava | Optional | study plan | |||||

2011/2012 | (N2647) Information and Communication Technology | (1103T031) Computational Mathematics | P | Czech | Ostrava | 1 | Optional | study plan | ||||

2011/2012 | (N2647) Information and Communication Technology | (1103T031) Computational Mathematics | K | Czech | Ostrava | 1 | Optional | study plan | ||||

2010/2011 | (N2647) Information and Communication Technology | (1103T031) Computational Mathematics | P | Czech | Ostrava | 1 | Optional | study plan | ||||

2010/2011 | (N2647) Information and Communication Technology | (1103T031) Computational Mathematics | K | Czech | Ostrava | 1 | Optional | study plan |

Block name | Academic year | Form of study | Study language | Year | W | S | Type of block | Block owner |
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2019/2020 Summer |

2018/2019 Summer |

2017/2018 Summer |

2016/2017 Summer |

2015/2016 Summer |

2014/2015 Summer |

2013/2014 Summer |

2012/2013 Summer |