UIN1004 Graph Theory I

Faculty of Philosophy and Science in Opava
Winter 2018
Extent and Intensity
2/2/0. 6 credit(s). Type of Completion: zk (examination).
Teacher(s)
doc. RNDr. Luděk Cienciala, Ph.D. (lecturer)
doc. RNDr. Luděk Cienciala, Ph.D. (seminar tutor)
doc. RNDr. Lucie Ciencialová, Ph.D. (seminar tutor)
Guaranteed by
doc. RNDr. Luděk Cienciala, Ph.D.
Institute of Computer Science – Faculty of Philosophy and Science in Opava
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
there are 6 fields of study the course is directly associated with, display
Course objectives
In this course students learn the basic concepts of the proving techniques and possible applications of graph theory.
Syllabus
  • 1. Graphs and simple graphs, vertex degree.
    2. Subgraphs, graph representation by matrices, paths, cycles, connected and unconnected graphs.
    3. Trees.
    4. Special families of graphs - complete graphs, bipartite and multi-partite graphs, isomorphism and automorphism.
    5. Matching and covering, edge coloring, matching and covering in bipartite graphs, the algorithm of seeking unsaturated alternating paths.
    6. Vertex coloring, planar graphs.
    7. The four-colour problem, non/planar graphs, Euler graphs, maze-like tasks - Tarry's algorithm algorithm of Trémaux.
    8. Hamilton graphs.
    9. Directed graphs, tournaments , networks, flows and cuts.
    10.Algorithm to find the minimum spanning tree, Prim's algorithm , Kruskal's algorithm , General scheme of graph search.
    11.Bread-First search, Depth-First search, Backtracking.
Literature
    recommended literature
  • Cienciala, L., Ciencialová, L. Teorie grafů a grafové algoritmy. Slezská univerzita v Opavě, 2014. ISBN 978-80-7510-060-3. info
  • Even, S., Even, G. Graph algorithms, 2nd edition. New York Cambridge University Press, 2012. ISBN 978-0-521-51718-8. info
  • Bondy, A., Murty, U. S. R. Graph Theory. Springer, 2011. info
  • Merris, R. Graph Theory. New York : John Wiley, 2001. ISBN 0-471-38925-0. info
  • Fronček, D. Úvod do teorie grafů. Opava, FPF SU, 2000. info
  • Bollobas, B. Modern Graph Theory. New York, Springer, 1998. info
  • Diestel, R. Graph Theory. New York, Springer, 1997. info
  • Demel, J. Grafy. Praha, SNTL, 1988. info
  • Kolář, J. Grafy. Praha, ČVUT, 1984. info
  • Kolář, J. Grafy - cvičení. Praha, ČVUT, 1984. info
  • Bosák, J. Grafy a ich aplikácie. Bratislava, Alfa, 1980. info
  • Behzad, M., Chartrand, G. Graphs and Digraphs. Weber, Schmidt, 1979. info
  • Bondy, J. A. Graph Theory with Applications. The Macmillan Press, 1976. info
Teaching methods
Interactive lecture
Lecture with a video analysis
Assessment methods
Exam
Language of instruction
Czech
Further comments (probably available only in Czech)
The course can also be completed outside the examination period.
Teacher's information
Total of examination exam can earn 60 points. For the successful completion students need to get 30 points.
The course is also listed under the following terms Winter 1993, Winter 1994, Winter 1995, Winter 1996, Winter 1997, Winter 1998, Winter 1999, Winter 2002, Winter 2003, Winter 2004, Winter 2005, Winter 2006, Winter 2007, Winter 2008, Winter 2009, Winter 2010, Winter 2011, Winter 2012, Winter 2013, Winter 2014, Winter 2015, Winter 2016, Winter 2017, Winter 2019, Winter 2020, Winter 2021, Winter 2022.
  • Enrolment Statistics (Winter 2018, recent)
  • Permalink: https://is.slu.cz/course/fpf/winter2018/UIN1004