Summary of the Graph Theory Exercises booklet

1. Basic concepts
   1. Graphs
   2. Bipartite graphs
   3. Neighborhoods and degrees of vertices
   4. Paths and circuits
   5. Union and intersection of graphs
   6. Planar graphs
   7. Subgraphs
   8. Cuts
   9. Paths and circuits in graphs
   10. Connected graphs
   11. Components
   12. Bridges
   13. Edge-biconnected graphs
   14. Articulations and biconnected graphs
   15. Forests and trees
   16. Minors of graphs
   17. Plane maps and their faces
   18. Random graphs
2. Isomorphism
3. Synthesis of graphs with given degrees
4. Bicolorable graphs
5. Stable sets
6. Cliques
7. Vertex covers
8. Vertex colorings
9. Matchings
10. Matchings in bipartite graphs
11. Matchings in arbitrary graphs
12. Edge colorings
13. Connectors and acyclic sets
14. Shortests paths and circuits
15. Flows
16. Internally disjoint flows
17. Hamiltonian circuits and paths
18. Circuit covers (Eulerian cycles)
19. Characterization of planarity

• Appendix A: Hints for some exercises
• Appendix B: Greek alphabet
• Bibliography
• Index

The material should be studied in the following order: