457-0305/01 – Graph Theory (TG)

Gurantor departmentDepartment of Applied MathematicsCredits4
Subject guarantordoc. Mgr. Petr Kovář, Ph.D.Subject version guarantordoc. RNDr. Dalibor Fronček, CSc., Ph.D.
Study levelundergraduate or graduateRequirementChoice-compulsory
Year2Semestersummer
Study languageCzech
Year of introduction2003/2004Year of cancellation2009/2010
Intended for the facultiesFEIIntended for study typesFollow-up Master
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 2+2

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. Fronček: Úvod do teorie grafů, Slezská univerzita Opava, (1999). J. Matoušek, J. Nešetřil, Chapters in Discrete Mathematics, Karolinum Praha (2000).

Recommended literature:

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

Way of continuous check of knowledge in the course of semester

E-learning

Other requirements

Prerequisities

Subject has no prerequisities.

Co-requisities

Subject has no co-requisities.

Subject syllabus:

1. Průměr, poloměr a obvod grafu. 2. Hranové grafy. Definice a konstrukce hranových grafů. Charakteristika hranových grafů. 3. Samokomplementární grafy. Komplement grafu. Vztah mezi průměrem grafu a jeho komplementem. Konstrukce nekonečných tříd samokomplementárních grafů. 4. Rozklady grafů. Rozklady kompletních grafů na izomorfní faktory. Rozklady grafů na faktory s danými průměry. Rozklady kompletních multiparitních grafů. 5. Problém rekonstrukce grafů. 6. Ramseyova teorie. Extremální teorie grafů. Ramseyova čísla. Zobecněná Ramseyova čísla. Další podobné problémy. 7. Grafy a grupy. Grupa amorfismu grafu. Grupa hranového automorfismu grafu. Cayleyho grafy. 8. Grafy s předepsaným okolím. Grafy s konstantním okolím. Extremální problémy. 9. Hypergrafy a designy. Hypergrafy, k uniformní hypergrafy. Designy. 10. Náhodné grafy. Enumerace grafů.

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 pointsMax. počet pokusů
Exercises evaluation and Examination Credit and Examination 100 (145) 51 3
        Examination Examination 100  0 3
        Exercises evaluation Credit 45  0 3
Mandatory attendence participation:

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

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Occurrence in study plans

Academic yearProgrammeBranch/spec.Spec.ZaměřeníFormStudy language Tut. centreYearWSType of duty
2003/2004 (N2646) Information Technology (1103T021) Computational Mathematics P Czech Ostrava 2 Choice-compulsory study plan
2003/2004 (N2646) Information Technology (1103T021) Computational Mathematics K Czech Ostrava 2 Choice-compulsory study plan

Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner

Assessment of instruction

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