# 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 theoryAre able to apply graph theoretical concepts to solve practical problemsUsed the example of graph theroretic topics to attain experience in self-contained scientific working Contents: Basic concepts, graphs, connectivity, treesMatchings, colorings, flowsHall's theorem, König's theorem, chromatic number, Menger's theoremPlanar graphs, Euler characteristic, Kuratowski's theorem, duality, cycle basesEthical responsibility in the application of models, algorithms and results Recommended Prerequisites: Knowledge of the content of the modules11101: Lineare Algebra und analytische Geometrie I11102: Lineare Algebra und analytische Geometrie II or11112: 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. OROral 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 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 extendStudy 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 TheoryAccompanying exercisesRelated examination Components to be offered in the Current Semester: 130496 Examination Graph Theory (Wiederholung)