470-6302/01 – 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
Study languageCzech
Year of introduction2010/2011Year of cancellation
Intended for the facultiesFEI, HGFIntended 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 Examination 28+0
Combined Examination 28+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

Active participation during lectures. Project - progress consulting. The exam has a written and oral part.

E-learning

Další požadavky na studenta

No additional requirements are imposed on the student.

Prerequisities

Subject has no prerequisities.

Co-requisities

Subject has no co-requisities.

Subject syllabus:

Lectures 1) Graphs, simple graphs. Subgraphs. Degree, Incidence matrix and adjacency matrix 2) Paths and cycles. Distance and eccentricity. 3) Trees, spanning trees, bipartite graphs. 4) Graph isomorphisms, automorphisms. 5) Connectivity, cuts, bridges, blocks, articulations. 6) Matching and covers in graphs and bipartite graphs, assignment problem, perfect matching. 7) Edge coloring and its applications. Chromatic index. Vizing theorem. 8) Vertex coloring and its applications. Chromatic number. Brooks theorem. 9) Planar graphs and their applications. Euler formula. Kuratowski hteorem, Four color theorem. 10) Nonplanar graph, nonplanarity measures 11) Eulerian and a hamiltonian graphs. 12) Oriented graphs. Oriented paths, cycles and tournaments. 13) Flows in a network, cuts. Maximum flow and minimum cut theorem. 14) Further advanced topics. During the semester each student prepares one or two projects.

Conditions for subject completion

Full-time form (validity from: 2009/2010 Winter semester, validity until: 2012/2013 Summer semester)
Task nameType of taskMax. number of points
(act. for subtasks)
Min. number of points
Examination Examination  
        Project Project  
        Written and theoretical exam Written examination  
Mandatory attendence parzicipation:

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