457-0925/01 – Graph Theory I (TGI)

Gurantor departmentDepartment of Applied MathematicsCredits10
Subject guarantordoc. Mgr. Petr Kovář, Ph.D.Subject version guarantordoc. Mgr. Petr Kovář, Ph.D.
Study levelpostgraduateRequirementChoice-compulsory
YearSemesterwinter + summer
Study languageCzech
Year of introduction1995/1996Year of cancellation2009/2010
Intended for the facultiesFEIIntended for study typesDoctoral
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+0
Combined Credit and Examination 2+0

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). In the course are many real life problems solved by the methods of graph theory.

Compulsory literature:

D. B. West, Introduction to graph theory - 2nd ed., Prentice-Hall, Upper Saddle River NJ, (2001), ISBN 0-13-0144400-2.

Recommended literature:

Bondy, U.S.R. Murty: Graph Theory with Applications, American Esevier Publishing Co., New York, 1976, ISBN 0-444-19451-7. Behzad, G. Chartrand, L. Lesniak-Foster: Graphs and Digraphs, Prindle, Weber and Schmid, Boston, 197, ISBN 0-87150-261-5.

Way of continuous check of knowledge in the course of semester

E-learning

Další požadavky na studenta

Prerequisities

Subject has no prerequisities.

Co-requisities

Subject has no co-requisities.

Subject syllabus:

Přednášky: Grafy a jednoduché grafy. Isomorfismus grafů. Incidenční matice a matice sousednosti. Podgrafy. Stupeň vrcholu. Cesty a cykly. Stromy, mosty a oddělující množiny(řezy). Artikulace. Souvislost grafů, bloky. Párování a pokrytí v grafech a biparitních grafech. Perfektní párování. Hranové barvení. Chromatický index grafu. Vizingova věta. Vrcholové barvení. Chromatické číslo grafu. Brooksova věta. Rovinné grafy. Duální graf. Eulerův vzorec. Kuratowského věta, věta o čtyřech barvách. Orientované grafy. Orientované cesty, orientované cykly. Toky v sítích, řezy. Věta o maximálním toku a minimálním řezu. Eulerovské a Hamiltonovské grafy.

Conditions for subject completion

Full-time form (validity from: 1960/1961 Summer semester, validity until: 2012/2013 Summer semester)
Task nameType of taskMax. number of points
(act. for subtasks)
Min. number of points
Exercises evaluation and Examination Credit and Examination 100 (145) 51
        Examination Examination 100  0
        Exercises evaluation Credit 45  0
Mandatory attendence parzicipation:

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2003/2004 (P2645) Electrical Engineering, Communication and Computer systems (3907V001) Electrical Power Engineering P Czech Ostrava Choice-compulsory study plan
2003/2004 (P2646) Information Technology (1801V002) Computer Science and Applied Mathematics P Czech Ostrava Choice-compulsory study plan
2003/2004 (P2645) Electrical Engineering, Communication and Computer systems (2612V045) Technical Cybernetics P Czech Ostrava Choice-compulsory study plan
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2002/2003 (P2612) Electrical Engineering and Computer Science (3907V001) Electrical power Engineering P Czech Ostrava Choice-compulsory study plan
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2001/2002 (P2612) Electrical Engineering and Computer Science (3907V001) Electrical power Engineering P Czech Ostrava Choice-compulsory study plan
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