Graph Theory, 6 credits

Grafteori, 6 hp

TATA64

Main field of study

Mathematics Applied Mathematics

Course level

Second cycle

Course type

Programme course

Examiner

Armen Asratian

Director of studies or equivalent

Jesper Thorén

Education components

Preliminary scheduled hours: 48 h
Recommended self-study hours: 112 h

Available for exchange students

Yes
Possible deviation from course syllabus/programme syllabus
ECV = 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 Mathematics

Course level

Second cycle

Advancement level

A1X

Course 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

TEN1Written examination6 creditsU, 3, 4, 5

Grades

Four-grade scale, LiU, U, 3, 4, 5

Department

Matematiska institutionen

Director of Studies or equivalent

Jesper Thorén

Examiner

Armen Asratian

Education components

Preliminary scheduled hours: 48 h
Recommended 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. 

Student rights and obligations (login required)
Linköping University common rules and regulations (in Swedish)
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.

Download

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)
X
X
X
 

                            		
                        

                        

                            
                            1.2 Fundamental engineering knowledge (G1X level)
                            
                                
 

                            		
                            
                                
 

                            		
                            
                                
 

                            		
                            
                            
                            
                                

                            		
                        

                        

                            
                            1.3 Further knowledge, methods, and tools in one or several subjects in engineering or natural science (G2X level)
                            
                                
 

                            		
                            
                                
 

                            		
                            
                                
 

                            		
                            
                            
                            
                                

                            		
                        

                        

                            
                            1.4 Advanced knowledge, methods, and tools in one or several subjects in engineering or natural sciences (A1X level)
                            
                                
 

                            		
                            
                                
 

                            		
                            
                                
 

                            		
                            
                            
                            
                                

                            		
                        

                        

                            
                            1.5 Insight into current research and development work
                            
                                
 

                            		
                            
                                
 

                            		
                            
                                
 

                            		
                            
                            
                            
                                

                            		
                        

                    
                    
                        

                            
                                2. PERSONAL AND PROFESSIONAL SKILLS AND ATTRIBUTES
                            
                        

                    
                    
                        

                            
                            2.1 Analytical reasoning and problem solving
                            
                                
 

                            		
                            
                                
X

                            		
                            
                                
X

                            		
                            
                            
                            
                                

                            		
                        

                        

                            
                            2.2 Experimentation, investigation, and knowledge discovery
                            
                                
 

                            		
                            
                                
 

                            		
                            
                                
X

                            		
                            
                            
                            
                                

                            		
                        

                        

                            
                            2.3 System thinking
                            
                                
 

                            		
                            
                                
 

                            		
                            
                                
 

                            		
                            
                            
                            
                                

                            		
                        

                        

                            
                            2.4 Attitudes, thought, and learning
                            
                                
 

                            		
                            
                                
X

                            		
                            
                                
X

                            		
                            
                            
                            
                                

                            		
                        

                        

                            
                            2.5 Ethics, equity, and other responsibilities
                            
                                
 

                            		
                            
                                
 

                            		
                            
                                
 

                            		
                            
                            
                            
                                

                            		
                        

                    
                    
                        

                            
                                3. INTERPERSONAL SKILLS: TEAMWORK AND COMMUNICATION
                            
                        

                    
                    
                        

                            
                            3.1 Teamwork
                            
                                
 

                            		
                            
                                
 

                            		
                            
                                
 

                            		
                            
                            
                            
                                

                            		
                        

                        

                            
                            3.2 Communications
                            
                                
 

                            		
                            
                                
 

                            		
                            
                                
X

                            		
                            
                            
                            
                                

                            		
                        

                        

                            
                            3.3 Communication in foreign languages
                            
                                
 

                            		
                            
                                
 

                            		
                            
                                
 

                            		
                            
                            
                            
                                

                            		
                        

                    
                    
                        

                            
                                4. CONCEIVING, DESIGNING, IMPLEMENTING AND OPERATING SYSTEMS IN THE ENTERPRISE, SOCIETAL AND ENVIRONMENTAL CONTEXT
                            
                        

                    
                    
                        

                            
                            4.1 External, societal, and environmental context
                            
                                
 

                            		
                            
                                
 

                            		
                            
                                
 

                            		
                            
                            
                            
                                

                            		
                        

                        

                            
                            4.2 Enterprise and business context
                            
                                
 

                            		
                            
                                
 

                            		
                            
                                
 

                            		
                            
                            
                            
                                

                            		
                        

                        

                            
                            4.3 Conceiving, system engineering and management
                            
                                
 

                            		
                            
                                
 

                            		
                            
                                
 

                            		
                            
                            
                            
                                

                            		
                        

                        

                            
                            4.4 Designing
                            
                                
 

                            		
                            
                                
 

                            		
                            
                                
 

                            		
                            
                            
                            
                                

                            		
                        

                        

                            
                            4.5 Implementing
                            
                                
 

                            		
                            
                                
 

                            		
                            
                                
 

                            		
                            
                            
                            
                                

                            		
                        

                        

                            
                            4.6 Operating
                            
                                
 

                            		
                            
                                
 

                            		
                            
                                
 

                            		
                            
                            
                            
                                

                            		
                        

                    
                    
                        

                            
                                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
                            
                                
 

                            		
                            
                                
 

                            		
                            
                                
 

                            		
                            
                            
                            
                                

                            		
                        

                        

                            
                            5.2 Economic conditions for knowledge development
                            
                                
 

                            		
                            
                                
 

                            		
                            
                                
 

                            		
                            
                            
                            
                                

                            		
                        

                        

                            
                            5.3 Identification of needs, structuring and planning of research or development projects
                            
                                
 

                            		
                            
                                
 

                            		
                            
                                
 

                            		
                            
                            
                            
                                

                            		
                        

                        

                            
                            5.4 Execution of research or development projects
                            
                                
 

                            		
                            
                                
 

                            		
                            
                                
 

                            		
                            
                            
                            
                                

                            		
                        

                        

                            
                            5.5 Presentation and evaluation of research or development projects
                            
                                
 

                            		
                            
                                
 

                            		
                            
                                
 

                            		
                            
                            
                            
                                

                            		
                        

                    
            

        




            

        

            


        

            
This tab contains public material from the course room in Lisam. The information published here is not legally binding, such material can be found under the other tabs on this page.


There are no files available for this course.