UIN1004 Graph Theory

Faculty of Philosophy and Science in Opava
Winter 2013
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)
Mgr. Martina Foldynová (seminar tutor)
Mgr. Adam Kožaný (seminar tutor)
Mgr. Marek Menšík, Ph.D. (seminar tutor)
RNDr. Michal Perdek (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 7 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 (in Czech)
  • 1. Grafy a jednoduché grafy, stupeň vrcholu.
    2. Podgrafy, reprezentace grafů pomocí matic, cesty, cykly, dosažitelnost, souvislost, souvislé, nesouvislé grafy, vzdálenost v grafu, excentricita vrcholu, průměr a poloměr grafu.
    3. Stromy, třídy grafů.
    4. Další třídy grafů - kompletní grafy, bipartitní a multi-partitní grafy, izomorfismus, automorfismus. Vrcholová a hranová souvislost, bloky.
    5. Párování, pokrytí, hranové barvení grafů, párování a pokrytí v bipartitních grafech, algoritmus hledající nesaturované alternující cesty.
    6. Vrcholové barvení grafů, planární grafy.
    7. Problém 4 barev, Neplanární grafy, Eulerovské grafy, Úlohy typu bludiště - Tarryho algoritmus, Trémauxův algoritmus.
    8. Hamiltonovské grafy, orientované grafy.
    9. Orientované grafy, turnaje, sítě, toky a řezy.
    10. Algoritmus nalezení minimální kostry grafu, Primův algoritmus, Kruskalův, Obecné schéma prohledávání grafu - značkování vrcholů.
    11. Prohledávání grafů do šířky, do hloubky, Backtracking.
Literature
    recommended literature
  • 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
Language of instruction
Czech
Further Comments
The course can also be completed outside the examination period.
Teacher's information
Credit: full-time students wrote the exercises two credit tests scoring 20 points each.
Exam: Total of examination exam can earn 60 points. For the successful completion students need to get 30 points. Mark for full-time study is determined by adding the points for the exam and points that the student earned during the semester in the course. Mark the combined study is determined from the points gained from examination test.
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 2014, Winter 2015, Winter 2016, Winter 2017, Winter 2018, Winter 2019, Winter 2020, Winter 2021, Winter 2022.
  • Enrolment Statistics (Winter 2013, recent)
  • Permalink: https://is.slu.cz/course/fpf/winter2013/UIN1004