Universitatea Babeş-Bolyai Cluj-Napoca
Facultatea de Matematică şi Informatică
Ciclul de studii: Licenţă
Domeniul: Calculatoare şi tehnologia informaţiei
Programul de studii: Ingineria informatiei - in limba engleza
Limba de predare: Engleză

SYLLABUS

I. General data
Code	Subject	
MIG0003	Discrete Mathematics	

Semester	Hours: C+S+L	Category	Status	
1	2+1+0	fundamental	compulsory	

II. Full status faculty members
Name and	Scientific	Didactic	Chair	Type of activity	
Surname	title	title		C	S	L	
LUPSA Radu	Ph.D.	Lect.	Computer Systems	*			

Associated faculty members
Name and	Scientific	Institution	Type of	Type of activity	
Surname	title		position	C	S	L	

III. Course objectives
The main objective is to introduce the students in the graph theoretical concepts and using these concepts in the problem modelling. The second one is the presentation and programming of the  main graph threoretical algorithms	

IV. Course contents
1. Introductory notions (grahs, directed graphs, subgrahs, paths, cycles, circuits, conectivity)
2. Paths problems: shortest path problem (algorithms: Moore-Dijkstra, Bellman-Kalaba, Ford, Floyd-Hu, Dantzig, Floyd-Hu-Warshall), Critical Path Method, Eulerian path, Hamiltonisan path. 
3. Fundamental numbers in graph theory (internal stability number, external stability number, algorithms, cromatic number, cyclomatic number)
4. Tress and forests (Kruskal's and Prim's algorithms) 
5. Planarity in graphs
6. Flows in networks  (algorithm of Ford-Fulkerson, extensions).
7. Matching problems
8. Extremal problems (theorems of Ramsey and Turán)
9. Counting and enumerating problems		

V. Bibliography
1. BERGE C., Graphes et hypergraphes, Dunod, Paris 1970.
2. B. ANDRÁSFAI: Introductory graph theory, Akadémiai Kiadó - North Holland, 1987.
3. BERGE C., Teoria grafurilor si aplicatiile ei, Ed. Tehnica, 1972 
4. T. TOADERE: Grafe. Teorie, algoritmi si aplicatii , Ed. Albastra, Cluj-N., 2002 
5. KÁSA ZOLTÁN: Combinatiroca cu aplicatii, Presa Universitara Clujeana, 2003.
6. CORMEN, LEISERSON, RIVEST: Introducere in algoritmi, Editura Computer Libris Agora,    2000.
7. ROSU A.: Teoria grafelor, algoritmi, aplicatii. Ed. Milit.1974 

Culegeri de probleme:
1. KÁSA Z., TARTIA C., TAMBULEA L.: Culegere de probleme de teoria grafelor, Lito. Univ.   Cluj-Napoca 1979. 
2. CATARANCIUC S., IACOB M.E., TOADERE T., Probleme de teoria grafelor, Lito. Univ.   Cluj-Napoca, 1994. 
3. TOMESCU I., Probleme de combinatorica si teoria grafurilor. Ed. Did. si Pedag. Bucuresti 1981.	

VI. Thematic of didactic activities per weeks
•	basic graph theory definitions (graph, multigraph, directed graph/multigraph, walk, trail, path), representations; week 1-2.
•	path-related problems: connected and strongly-connected graphs, connected components, shortest path, Moore, Bellman-Kalaba, Dijkstra, Floyd-Warshal algorithms; week 3-4.
•	partial ordering, critical path; topological sorting and PERT method; week 5-6.
•	trees and forests; Kruskal and Prim algorithms; graph traversal and applications; week 7.
•	hard problems (clique, independent set, vertex covering, coloring, Hamiltonian cycle, traveling salesman problem); weeks 8-9
•	Eulerian cycle; week 10
•	planar graph; week 10
•	transport networks and flows; maximum flow problems; matching problems; week 11-12
•	counting and enumerating problems; week 13-14
•	 extremal problems; week 14		

VII. Didactic methods used
expuneri orale, cu exemple; discutii (interactive) in timpul orelor de curs (in masura posibilitatilor) si de laborator; exercitii individuale, teoretice si practice, in timpul orelor de laborator	

VIII. Assessment
Written exam
See also: http://www.cs.ubbcluj.ro/~rlupsa/edu/grafe/	

IX. Additional references
http://www.cs.ubbcluj.ro/~rlupsa/edu/grafe/	

	Dean,							Chair head,

	Date,							Course responsible,
								Lect. LUPSA Radu, Ph.D.