Table of Contents


You can download the book as a PDF, or click the links below to read the book online.


  1. The Beginning
    1. Modeling problems with graphs
    2. Isomorphisms and subgraphs
    3. Walks, paths, and cycles
    4. The degree of a vertex
  2. Vertex Degrees
    1. Regular graphs
    2. Graphic sequences
    3. Multigraphs and digraphs
    4. Euler tours
  3. Trees
    1. Trees and spanning trees
    2. Properties of trees
    3. Cayley's formula
    4. Directed acyclic graphs
  4. Matchings
    1. Bipartite graphs
    2. Kőnig's theorem
    3. Hall's theorem
    4. Matchings in general graphs
  5. Hard Problems
    1. Hamilton cycles
    2. Cliques and independent sets
    3. Graph coloring
    4. Line graphs
  6. Planar Graphs
    1. Planar graphs
    2. Planarity testing
    3. Polyhedra
    4. Coloring maps
  7. Connectivity
    1. Cut vertices
    2. Connectivity
    3. Menger's theorem
    4. Maximum flows
  8. Appendix
    1. Review of proof-writing
    2. Proof by induction
    3. Bibliography

Start Doing Graph Theory © 2025 by Mikhail Lavrov is licensed under CC BY-SA 4.0