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Topic of choice II - Graph theory


Some basic information about the module

Cycle of education:
2018/2019
The name of the faculty organization unit:
The faculty Mathematics and Applied Physics
The name of the field of study:
Mathematics
The area of study:
sciences
The profile of studing:
The level of study:
second degree study
Type of study:
full time
discipline specialities :
Applications of Mathematics in Computer Science, Applications of Mathematics in Economics
The degree after graduating from university:
The name of the module department :
Departament of Discrete Mathematics
The code of the module:
4059
The module status:
mandatory for teaching programme with the posibility of choice Applications of Mathematics in Economics
The position in the studies teaching programme:
sem: 3 / W30 C30 / 4 ECTS / Z
The language of the lecture:
Polish
The name of the coordinator:
Dorota Bród, PhD
office hours of the coordinator:
terminy konsultacji na stronie domowej

The aim of studying and bibliography

The main aim of study:
A student knows advanced methods of graph theory

The general information about the module:
Topics discused in the module: independence, domination, colouring of graphs

Bibliography required to complete the module
Bibliography used during lectures
1 R. Diestel Graph theory Springer-Verlag, Heidelberg, New York. 2005
2 Z. Palka, A. Ruciński Niekonstruktywne metody matematyki dyskretnej WNT, Warszawa. 1996
Bibliography used during classes/laboratories/others
1 Z. Palka, A. Ruciński Niekonstruktywne metody matematyki dyskretnej WNT, Warszawa. 1996
2 R. Diestel Graph theory Springer-Verlag, Heidelberg, New York. 2005
Bibliography to self-study
1 C. Berge Graphs and hypergraphs North-Holland Publishing Company. 1976

Basic requirements in category knowledge/skills/social competences

Formal requirements:
Requirements accordant with Rules and Regulations of studies

Basic requirements in category knowledge:
a student knows basic definitions of graph theory

Basic requirements in category skills:
a student knows some methods of discrete mathematics and their applications

Basic requirements in category social competences:
a student can work in group

Module outcomes

MEK The student who completed the module Types of classes / teaching methods leading to achieving a given outcome of teaching Methods of verifying every mentioned outcome of teaching Relationships with KEK Relationships with OEK
MEK01 A student knows basic definitions and theorems of graph theory lecture, classes test K-W01+
K-W05+
K-U02+
K-U04+
 W01
W02
U03
U05
MEK02 A student knows basic and advance methods of graph theory lecture, classes test K-W04+
K-U02+
K-U03+
K-K02+
K-K07+
 U01
U02
U03
U05
K01
K02
K06
MEK03 A student can use methods of graph theory for solving of discrete problems lecture, classes test K-W07+
K-U04+
K-K01+
K-K04+
 W02
U03
U07
K01
K03
K04

The syllabus of the module

Sem. TK The content realized in MEK
3 TK01 Basic concepts of graph theory W01, W02, C01, C02 MEK01
3 TK02 Products of graphs and their generalizations. W03, C03 MEK01 MEK02
3 TK03 Independence in graphs. Independence number. Counting of independent sets in some classes of graphs. W04, W05, C04, C05, C06 MEK01 MEK02
3 TK04 Graph parameters and their connections with independence number. W06, W07, W08, C07, C09 MEK01 MEK03
3 TK05 Domination in graphs. Domination number. Counting of dominating sets in some classes of graphs. Kernels in graphs, (k,l)-kernels. W09, W10, W11, C10, C11, C12 MEK01 MEK03
3 TK06 Colouring of graphs. Colouring of vertices and edges, mix colouring. Chromatic polynomial and its properties. W12, W13, W14, W15, C13, C14 MEK01 MEK03
3 TK07 Tests C8, C15 MEK01 MEK02 MEK03

The student's effort

The type of classes The work before classes The participation in classes The work after classes
Lecture (sem. 3) The preparation for a test: 10.00 hours/sem.
 contact hours: 30.00 hours/sem.
 complementing/reading through notes: 5.00 hours/sem.
Studying the recommended bibliography: 5.00 hours/sem.
Class (sem. 3) The preparation for a Class: 5.00 hours/sem.
The preparation for a test: 10.00 hours/sem.
 contact hours: 30.00 hours/sem.
 Finishing/Studying tasks: 5.00 hours/sem.
Advice (sem. 3)
Credit (sem. 3)

The way of giving the component module grades and the final grade

The type of classes The way of giving the final grade
Lecture A credit for the lecture is based on attendance at the lectures.
Class Student has to get at lesat 50% points on the tests during classes.
The final grade

Sample problems

Required during the exam/when receiving the credit
(-)

Realized during classes/laboratories/projects
(-)

Others
(-)

Can a student use any teaching aids during the exam/when receiving the credit : no

The contents of the module are associated with the research profile no