Gurantor department | Department of Applied Mathematics | Credits | 4 |

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

Study level | undergraduate or graduate | Requirement | Choice-compulsory |

Year | 2 | Semester | summer |

Study language | Czech | ||

Year of introduction | 2016/2017 | Year of cancellation | 2020/2021 |

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

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

Login | Name | Tuitor | Teacher giving lectures |

KOV16 | doc. Mgr. Petr Kovář, Ph.D. | ||

KUB59 | RNDr. Michael Kubesa, 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:
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 and 14) Further topics: flows in networks, cuts. Maximal flow and minimal cut Theorem. Graph models.
Discussions:
1) Graphs, simple graphs. Degree of a vertex.
2) Paths and cycles. Important graph classes.
3) Trees, bridges and cuts.
4) Graph isomorphisms.
5) Graph connectivity, blocks and articulations.
6) Matching and covers in general and bipartite graphs. Perfect matchings.
7) Edge colorings. Chromatic index.
8) Vertex colorings, Chromatic number.
9) Planar graphs. Euler's formula for general planar graphs.
10) Non-planar graphs, measures of non-planarity.
11) Eulerian and Hamiltonian graphs.
12) Oriented graphs. Oriented paths and cycles.
13 and 14) Further topics; graph models and their limits.
During the semester each student prepares one or two projects. Topic of each project is chosen among topics presented in the lecture. Assignments are available on the instructor webpage or in the university electronic information system, for example:
1) planar graphs and their applications
2) graph colorings and their applications
For a pass it is necessary to have at least one project graded for at least 10 points.

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

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

Credit | Credit | 20 | 10 | |

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

Written part | Written examination | 60 | 30 | |

Theory part of the exam | Oral examination | 20 | 5 |

Show history

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

Show history

Academic year | Programme | Branch/spec. | Spec. | Zaměření | Form | Study language | Tut. centre | Year | W | S | Type of duty | |
---|---|---|---|---|---|---|---|---|---|---|---|---|

2018/2019 | (N2658) Computational Sciences | (2612T078) Computational Sciences | P | Czech | Ostrava | 2 | Choice-compulsory | study plan | ||||

2017/2018 | (N2658) Computational Sciences | (2612T078) Computational Sciences | P | Czech | Ostrava | 2 | Choice-compulsory | study plan | ||||

2016/2017 | (N2658) Computational Sciences | (2612T078) Computational Sciences | P | Czech | Ostrava | 2 | Choice-compulsory | study plan |

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