14085 - Graph Theory Modulübersicht

Module Number: 14085
Module Title:Graph Theory
  Graphentheorie
Department: Faculty 1 - Mathematics, Computer Science, Physics, Electrical Engineering and Information Technology
Responsible Staff Member:
  • Prof. Dr. rer. nat. habil. Köhler, Ekkehard
Language of Teaching / Examination:English
Duration:1 semester
Frequency of Offer: Each winter semester odd year
Credits: 8
Learning Outcome:The students
  • Know the most important terms and connections of graph theory
  • Are able to apply graph theoretical concepts to solve practical problems
  • Used the example of graph theroretic topics to attain experience in self-contained scientific working
Contents:
  • Basic concepts, graphs, connectivity, trees
  • Matchings, colorings, flows
  • Hall's theorem, König's theorem, chromatic number, Menger's theorem
  • Planar graphs, Euler characteristic, Kuratowski's theorem, duality, cycle bases
  • Ethical responsibility in the application of models, algorithms and results
Recommended Prerequisites:Knowledge of the content of the modules
  • 11101: Lineare Algebra und analytische Geometrie I
  • 11102: Lineare Algebra und analytische Geometrie II
or
  • 11112: Mathematik IT-1 (Diskrete Mathematik)
  • 11113: Mathematik IT-2 (Lineare Algebra)
Mandatory Prerequisites:
  • No successful participation in module 11415 Graphtheorie
Forms of Teaching and Proportion:
  • Lecture / 4 Hours per Week per Semester
  • Exercise / 2 Hours per Week per Semester
  • Self organised studies / 150 Hours
Teaching Materials and Literature:
  • D.B. West: Introduction to Graph Theory. (Prentice Hall, 1996)
  • R. Diestel: Graphentheorie. (Springer,1996)
Module Examination:Final Module Examination (MAP)
Assessment Mode for Module Examination:
  • Written examination, 90 min. OR
  • Oral examination, 30 min.
In the first lecture it will announced, wether the examination will organized in written or oral form.
Evaluation of Module Examination:Performance Verification – graded
Limited Number of Participants:None
Part of the Study Programme:
  • Master (research-oriented) / Angewandte Mathematik / PO 2019
  • Master (research-oriented) / Artificial Intelligence / PO 2022
  • Bachelor (research-oriented) / Informatik / PO 2008
  • Master (research-oriented) / Informatik / PO 2008
  • Bachelor (research-oriented) / Künstliche Intelligenz / PO 2022
  • Master (research-oriented) / Künstliche Intelligenz Technologie / PO 2022
  • Bachelor (research-oriented) / Mathematik / PO 2019
  • Bachelor (research-oriented) / Mathematik / PO 2023
  • Bachelor (research-oriented) - Co-Op Programme with Practical Placement / Mathematik - dual / PO 2023
  • Bachelor (research-oriented) / Wirtschaftsmathematik / PO 2023
  • Bachelor (research-oriented) - Co-Op Programme with Practical Placement / Wirtschaftsmathematik - dual / PO 2023
Remarks:
  • Study programme Angewandte Mathematik M.Sc.: Compulsory elective module in complex „Analysis / Algebra / Kombinatorik“
  • Study programme Mathematik B.Sc.: Compulsory elective module in complex „Vertiefung“, in limited extend 
  • Study programme Wirtschaftsmathematik B.Sc.: Compulsory elective module in complex „Vertiefung“, in limited extend
  • Study programme Informatik B.Sc.: Compulsory elective module in  „Praktische Mathematik“ or in field of application „Mathematik“
  • Study programme Informatik M.Sc.: Compulsory elective module in „Mathematik“ or in field of application „Mathematik“
  • Study programme  Künstliche Intelligenz B.Sc.: Compulsory elective module in complex „Wissensakquise, -repräsentation und -verarbeitung“
  • Study programme  Künstliche Intelligenz Technologie M.Sc.: Compulsory elective module in complex „Software-basierte Systeme“
  • Study programme Artificial Intelligence M.Sc.: Compulsory elective module in complex „Knowledge Acquisition, Representation, and Processing“
  • Study programme Physics M.Sc.: Compulsory elective module in complex „Minor Subject“
Module Components:
  • Lecture: Graph Theory
  • Accompanying exercises
  • Related examination
Components to be offered in the Current Semester: