457-0043/01 – Graph Theory (TGR)

Gurantor departmentDepartment of Applied MathematicsCredits4
Subject guarantordoc. RNDr. Dalibor Fronček, CSc.,Ph.D.Subject version guarantordoc. RNDr. Dalibor Fronček, CSc.,Ph.D.
Study levelundergraduate or graduateRequirementCompulsory
Year2Semestersummer
Study languageCzech
Year of introduction1992/1993Year of cancellation2002/2003
Intended for the facultiesFEIIntended for study typesMaster
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Full-time Credit and Examination 2+2

Subject aims expressed by acquired skills and competences

Teaching methods

Summary

Graphs, simple graphs, subgraphs and isomorphism of graphs. Paths and cycles. Connected and disconnected graphs. Complete graphs, bipartite and multipartite graphs. Trees and spanning trees. Vertex and edge connectivity. Matchings and coverings, perfect matching. Edge coloring and chromatic index, vertex coloring and chromatic number. Planar graphs. Eulerian and Hamiltoniam graphs. Directed graphs. Tournaments and networks.

Compulsory literature:

Recommended literature:

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: 1. Grafy a jednoduché grafy. Isomorfismus grafů. Incidenční matice a matice sousednosti. Podgrafy. Stupeň vrcholu. Cesty a cykly. 2. Stromy, mosty a oddělující množiny (řezy). Artikulace. 3. Souvislost grafů, bloky. 4. Párování a pokrytí v grafech a biparitních grafech. Perfektní párování. 5. Hranové barvení. Chromatický index grafu. Vizingova věta. 6. Vrcholové barvení. Chromatické číslo grafu. Brooksova věta. 7. Rovinné grafy. Duální graf. Eulerův vzorech. Kuratowského věta, věta o čtyřech barvách. 8. Orientované grafy. orientované cesty, orientované cykly. 9. Toky v sítích, řezy. Věta o maxímálním toku a minimálním řezu. 10. Eulerovské a hamiltonovské grafy.

Conditions for subject completion

Full-time form (validity from: 1960/1961 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:

Show history

Occurrence in study plans

Academic yearProgrammeField of studySpec.FormStudy language Tut. centreYearWSType of duty
2005/2006 (M2612) Electrical Engineering and Computer Science (2612T999) Common Base for FEI P Czech Ostrava 2 Compulsory study plan
2004/2005 (M2612) Electrical Engineering and Computer Science (2612T999) Common Base for FEI P Czech Ostrava 2 Compulsory study plan
2003/2004 (M2612) Electrical Engineering and Computer Science (3902T023) Computer Science P Czech Ostrava 2 Compulsory study plan
2003/2004 (M2612) Electrical Engineering and Computer Science (2612T999) Common Base for FEI P Czech Ostrava 2 Compulsory study plan
2002/2003 (M2612) Electrical Engineering and Computer Science (2601T004) Measurement and Control Engineering P Czech Ostrava Choice-compulsory study plan
2002/2003 (M2612) Electrical Engineering and Computer Science (2612T018) Electronics and Communication Technology P Czech Ostrava Choice-compulsory study plan
2002/2003 (M2612) Electrical Engineering and Computer Science (2642T004) Electrical Machines, Apparatus and Drives (10) Elektrické stroje a přístroje P Czech Ostrava Choice-compulsory study plan
2002/2003 (M2612) Electrical Engineering and Computer Science (2642T004) Electrical Machines, Apparatus and Drives (20) Elektrické pohony a výkonová elektronika P Czech Ostrava Choice-compulsory study plan
2002/2003 (M2612) Electrical Engineering and Computer Science (3902T023) Computer Science P Czech Ostrava Choice-compulsory study plan
2002/2003 (M2612) Electrical Engineering and Computer Science (3907T001) Electrical Power Engineering P Czech Ostrava Choice-compulsory study plan
2002/2003 (M2612) Electrical Engineering and Computer Science (3902T023) Computer Science P Czech Ostrava 2 Compulsory study plan
2001/2002 (M2612) Electrical Engineering and Computer Science (2601T004) Measurement and Control Engineering P Czech Ostrava Choice-compulsory study plan
2001/2002 (M2612) Electrical Engineering and Computer Science (2612T018) Electronics and Communication Technology P Czech Ostrava Choice-compulsory study plan
2001/2002 (M2612) Electrical Engineering and Computer Science (2642T004) Electrical Machines, Apparatus and Drives (10) Elektrické stroje a přístroje P Czech Ostrava Choice-compulsory study plan
2001/2002 (M2612) Electrical Engineering and Computer Science (2642T004) Electrical Machines, Apparatus and Drives (20) Elektrické pohony a výkonová elektronika P Czech Ostrava Choice-compulsory study plan
2001/2002 (M2612) Electrical Engineering and Computer Science (3902T023) Computer Science P Czech Ostrava Choice-compulsory study plan
2001/2002 (M2612) Electrical Engineering and Computer Science (3907T001) Electrical Power Engineering P Czech Ostrava Choice-compulsory study plan
2001/2002 (M2612) Electrical Engineering and Computer Science (3902T023) Computer Science P Czech Ostrava 2 Compulsory study plan
2000/2001 (M2612) Electrical Engineering and Computer Science (3902T023) Computer Science P Czech Ostrava 2 Compulsory study plan

Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner