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Graph Theory, 6 credits
Grafteori, 6 hp
TATA64
Main field of study
Mathematics Applied MathematicsCourse level
Second cycleCourse type
Programme courseExaminer
Armen AsratianDirector of studies or equivalent
Jesper ThorénEducation components
Preliminary scheduled hours: 48 hRecommended self-study hours: 112 h
Available for exchange students
YesECV = Elective / Compulsory / Voluntary
| Course offered for | Semester | Period | Timetable module | Language | Campus | ECV | |
|---|---|---|---|---|---|---|---|
| 6CDDD | Computer Science and Engineering, M Sc in Engineering | 8 (Spring 2017) | 1, 2 | 2, 2 | English | Linköping, Valla | E |
| 6CMJU | Computer Science and Software Engineering, M Sc in Engineering | 8 (Spring 2017) | 1, 2 | 2, 2 | English | Linköping, Valla | E |
| 6MDAV | Computer Science, Master's programme | 2 (Spring 2017) | 1, 2 | 2, 2 | English | Linköping, Valla | E |
| 6MICS | Computer Science, Master's programme | 2 (Spring 2017) | 1 | 2 | English | Linköping, Valla | E |
| 6MICS | Computer Science, Master's programme | 2 (Spring 2017) | 2 | 2 | English | Linköping, Valla | E |
| 6CITE | Information Technology, M Sc in Engineering | 8 (Spring 2017) | 1, 2 | 2, 2 | English | Linköping, Valla | E |
| 6KMAT | Mathematics | 4 (Spring 2017) | 1, 2 | 2, 2 | English | Linköping, Valla | E |
| 6MMAT | Mathematics, Master's programme | 2 (Spring 2017) | 1, 2 | 2, 2 | English | Linköping, Valla | E |
| 6MMAT | Mathematics, Master's programme (Mathematics) | 2 (Spring 2017) | 1, 2 | 2, 2 | English | Linköping, Valla | E |
Main field of study
Mathematics, Applied MathematicsCourse level
Second cycleAdvancement level
A1XCourse offered for
- Computer Science and Software Engineering, M Sc in Engineering
- Mathematics, Master's programme
- Computer Science, Master's programme
- Mathematics
- Information Technology, M Sc in Engineering
- Computer Science and Engineering, M Sc in Engineering
Specific information
The course is only offered every second year. It will be offered during 2015.
Entry requirements
Note: Admission requirements for non-programme students usually also include admission requirements for the programme and threshold requirements for progression within the programme, or corresponding.
Prerequisites
Elementary courses in linear algebra and discrete mathematics.
Intended learning outcomes
To give good knowledge of graph theoretical concepts. And to practice how to use them in mathematics, natural science and computer science. After completing the course, students should:
- know important classes of problems in graph theory
- be able to formulate and prove fundamental theorems on trees, matchings, connectivity, colorings, plane and hamiltonian graphs
- be able to describe and apply some basic algorithms for graphs
- have a knowledge on elementary Ramsey theory
- be able to use graphs as a tool to model real-life problems
Course content
- Trees: Cayley’s formula, spanning trees and Edmonds’s algorithm for isomorphism of trees,
- Connectivity and Menger’s theorem,
- Hamilton cycles and colorings of graphs,
- Matchings and coverings, Tutte’s theorem on perfect matchings, Egervary's algorithm
- Elementary Ramsey theory
- Plane graphs: Euler’s formula, the five-color theorem, Grinberg’s formula
- Some applications of graphs in natural science, timetabling and computer science.
Teaching and working methods
Lectures and problem sessions.
The course runs over the entire spring semester.
Examination
| TEN1 | Written examination | 6 credits | U, 3, 4, 5 |
Grades
Four-grade scale, LiU, U, 3, 4, 5Department
Matematiska institutionenDirector of Studies or equivalent
Jesper ThorénExaminer
Armen AsratianEducation components
Preliminary scheduled hours: 48 hRecommended self-study hours: 112 h
Course literature
J.A.Bondy and U.S.R. Murty, Graph theory with applications (tillgänglig vid internet) R. Diestel, Graph Theory, 4th ed., 2010 (tillgänglig vid internet) Samt kompletterande material som utdelas under kursens gång.| Code | Name | Scope | Grading scale |
|---|---|---|---|
| TEN1 | Written examination | 6 credits | U, 3, 4, 5 |
Regulations (apply to LiU in its entirety)
The university is a government agency whose operations are regulated by legislation and ordinances, which include the Higher Education Act and the Higher Education Ordinance. In addition to legislation and ordinances, operations are subject to several policy documents. The Linköping University rule book collects currently valid decisions of a regulatory nature taken by the university board, the vice-chancellor and faculty/department boards.
LiU’s rule book for education at first-cycle and second-cycle levels is available at http://styrdokument.liu.se/Regelsamling/Innehall/Utbildning_pa_grund-_och_avancerad_niva.
Course literature is preliminary.
J.A.Bondy and U.S.R. Murty, Graph theory with applications (tillgänglig vid internet)
R. Diestel, Graph Theory, 4th ed., 2010 (tillgänglig vid internet)
Samt kompletterande material som utdelas under kursens gång.
Note: The course matrix might contain more information in Swedish.
I = Introduce, U = Teach, A = Utilize
| I | U | A | Modules | Comment | ||
|---|---|---|---|---|---|---|
| 1. DISCIPLINARY KNOWLEDGE AND REASONING | ||||||
| 1.1 Knowledge of underlying mathematics and science (G1X level) |
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| 1.2 Fundamental engineering knowledge (G1X level) |
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| 1.3 Further knowledge, methods, and tools in one or several subjects in engineering or natural science (G2X level) |
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| 1.4 Advanced knowledge, methods, and tools in one or several subjects in engineering or natural sciences (A1X level) |
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| 1.5 Insight into current research and development work |
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| 2. PERSONAL AND PROFESSIONAL SKILLS AND ATTRIBUTES | ||||||
| 2.1 Analytical reasoning and problem solving |
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| 2.2 Experimentation, investigation, and knowledge discovery |
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X
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| 2.3 System thinking |
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| 2.4 Attitudes, thought, and learning |
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| 2.5 Ethics, equity, and other responsibilities |
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| 3. INTERPERSONAL SKILLS: TEAMWORK AND COMMUNICATION | ||||||
| 3.1 Teamwork |
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| 3.2 Communications |
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| 3.3 Communication in foreign languages |
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| 4. CONCEIVING, DESIGNING, IMPLEMENTING AND OPERATING SYSTEMS IN THE ENTERPRISE, SOCIETAL AND ENVIRONMENTAL CONTEXT | ||||||
| 4.1 External, societal, and environmental context |
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| 4.2 Enterprise and business context |
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| 4.3 Conceiving, system engineering and management |
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| 4.4 Designing |
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| 4.5 Implementing |
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| 4.6 Operating |
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| 5. PLANNING, EXECUTION AND PRESENTATION OF RESEARCH DEVELOPMENT PROJECTS WITH RESPECT TO SCIENTIFIC AND SOCIETAL NEEDS AND REQUIREMENTS | ||||||
| 5.1 Societal conditions, including economic, social, and ecological aspects of sustainable development for knowledge development |
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| 5.2 Economic conditions for knowledge development |
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| 5.3 Identification of needs, structuring and planning of research or development projects |
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| 5.4 Execution of research or development projects |
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| 5.5 Presentation and evaluation of research or development projects |
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