Applications of LA in Combinatorics

Course completion requirements

It is required to attend all tutorials and submit solution to home assignments in order to pass the course tutorials. There are two types of homework:

1. *-type: Every week, one assignment will be posted and you have two weeks to finish it. To pass the tutorials, you have to submit at least half of the assignments.
2. a-type: If you do not attend tutorials, you have to submit homework assignments corresponding to the tutorials.

HW submission progress

Homework assignments

Date:	Topic:	Materials:	Deadline:
7. 10. 2022	Revision of Linear Algebra	here	21. 10. 2022
14. 10. 2022	Determinants and Odd/Even cities	here	28. 10. 2022
21. 10. 2022	Odd cities	here	4. 11. 2022
28. 10. 2022	National holiday	here	28. 10. 2022
4. 11. 2022	Mod-q cities	here	18. 11. 2022
11. 11. 2022	Spectral graph theory I.	here	25. 11. 2022
18. 11. 2022	Spectral graph theory II.	here	2. 12. 2022
25. 11. 2022	Spectral graph theory III.	here	16. 12. 2022
2. 12. 2022	Spectral graph theory IV.	here	16. 12. 2022
6. 12. 2022	Spectral graph theory V.	here	6. 1. 2023

Lectures

The lecture notes are avalaible only in Czech. For materials in English, contact prof. Kratochvil at honza@kam.mff.cuni.cz.

Date:	Topic:	Materials:
7. 10. 2022	Matrix representations of graphs, powers of the adjacency matrix, determinants and spanning trees	here
14. 10. 2022	Linear (in)dependece, sizes of special set systems, 2-distances sets	here
21. 10. 2022	Orthogonality and orthogonal complements, cycle space of a graph	here
28. 10. 2022	National holiday	here
4. 11. 2022	Linear forms, dual homomorphisms, Seidel switching	here
11. 11. 2022	Spectral graph theory, eigenvalues of graphs, Moore graphs	here
18. 11. 2022	Strongly regular graphs, friendship theorem, interlacing of eigenvalues	here
25. 11. 2022	Applications of interlacing of eigenvalues	here
2. 12. 2022	Shannon capacity of graphs	here
9. 12. 2022	Coding theory, Lloyd theorem	here