470-4302/01 – Graph Theory (TG)

Gurantor departmentDepartment of Applied MathematicsCredits6
Subject guarantordoc. Mgr. Petr Kovář, Ph.D.Subject version guarantordoc. Mgr. Petr Kovář, Ph.D.
Study levelundergraduate or graduateRequirementOptional
YearSemestersummer
Study languageCzech
Year of introduction2010/2011Year of cancellation
Intended for the facultiesFEIIntended for study typesFollow-up Master
Instruction secured by
LoginNameTuitorTeacher giving lectures
KOV16 doc. Mgr. Petr Kovář, Ph.D.
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Full-time Credit and Examination 2+2
Part-time Credit and Examination 10+10

Subject aims expressed by acquired skills and competences

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.

Teaching methods

Lectures
Individual consultations
Tutorials
Project work

Summary

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.

Compulsory literature:

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

Recommended literature:

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

Way of continuous check of knowledge in the course of semester

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.

E-learning

Other requirements

There are no other requirements.

Prerequisities

Subject has no prerequisities.

Co-requisities

Subject has no co-requisities.

Subject syllabus:

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.

Conditions for subject completion

Part-time form (validity from: 2011/2012 Summer semester)
Task nameType of taskMax. number of points
(act. for subtasks)
Min. number of pointsMax. 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
Mandatory attendence participation: participation at all exercises is obligatory, absence of 20% can be excused participation at all lectures is expected

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

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Occurrence in study plans

Academic yearProgrammeField of studySpec.ZaměřeníFormStudy language Tut. centreYearWSType 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

Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner

Assessment of instruction



2019/2020 Summer
2018/2019 Summer
2017/2018 Summer
2016/2017 Summer
2015/2016 Summer
2014/2015 Summer
2013/2014 Summer
2012/2013 Summer