Lectures
1) Graphs, simple graphs. Subgraphs. Degree, Incidence matrix and adjacency matrix
2) Paths and cycles. Distance and eccentricity.
3) Trees, spanning trees, bipartite graphs.
4) Graph isomorphisms, automorphisms.
5) Connectivity, cuts, bridges, blocks, articulations.
6) Matching and covers in graphs and bipartite graphs, assignment problem, perfect matching.
7) Edge coloring and its applications. Chromatic index. Vizing theorem.
8) Vertex coloring and its applications. Chromatic number. Brooks theorem.
9) Planar graphs and their applications. Euler formula. Kuratowski hteorem, Four color theorem.
10) Nonplanar graph, nonplanarity measures
11) Eulerian and a hamiltonian graphs.
12) Oriented graphs. Oriented paths, cycles and tournaments.
13) Flows in a network, cuts. Maximum flow and minimum cut theorem.
During the semester each student prepares one or two projects.
1) Graphs, simple graphs. Subgraphs. Degree, Incidence matrix and adjacency matrix
2) Paths and cycles. Distance and eccentricity.
3) Trees, spanning trees, bipartite graphs.
4) Graph isomorphisms, automorphisms.
5) Connectivity, cuts, bridges, blocks, articulations.
6) Matching and covers in graphs and bipartite graphs, assignment problem, perfect matching.
7) Edge coloring and its applications. Chromatic index. Vizing theorem.
8) Vertex coloring and its applications. Chromatic number. Brooks theorem.
9) Planar graphs and their applications. Euler formula. Kuratowski hteorem, Four color theorem.
10) Nonplanar graph, nonplanarity measures
11) Eulerian and a hamiltonian graphs.
12) Oriented graphs. Oriented paths, cycles and tournaments.
13) Flows in a network, cuts. Maximum flow and minimum cut theorem.
During the semester each student prepares one or two projects.