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
01	A student knows basic definitions and theorems of graph theory	lecture, classes	test	K_W01+ K_W05+ K_U02+ K_U04+	X2A_W01 X2A_W02 X2A_U03 X2A_U05
02	A student knows basic and advance methods of graph theory	lecture, classes	test	K_W04+ K_U02+ K_U03+ K_K02+ K_K07+	X2A_U01 X2A_U02 X2A_U03 X2A_U05 X2A_K01 X2A_K02 X2A_K06
03	A student can use methods of graph theory for solving of discrete problems	lecture, classes	test	K_W07+ K_U04+ K_K01+ K_K04+	X2A_W02 X2A_U03 X2A_U07 X2A_K01 X2A_K03 X2A_K04

Attention: Depending on the epidemic situation, verification of the achieved learning outcomes specified in the study program, in particular credits and examinations at the end of specific classes, can be implemented remotely (real-time meetings).

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	The final grade is the grade of classes.

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