Table of Contents:
  • Introduction and overview
  • Abstract and set systems
  • Simplicial topology
  • Discrete Morse theory
  • Decision trees
  • Miscellaneous results
  • Graph properties
  • Dihedral graph properties
  • Diagraph properties
  • Main goals and proof techniques
  • Matchings
  • Graphs of bounded degree
  • Forests and matroids
  • Bipartite graphs
  • Directed variants of forests and bipartite graphs
  • Noncrossing graphs
  • Non- Hamiltonian graphs
  • Disconnected graphs
  • Not 2-connected graphs
  • Not 3-connected graphs and beyond
  • Dihedral variants of k-connected graphs
  • Directed variants of connected graphs
  • Not 2-edge-connected graphs
  • Graphs avoiding k-matching
  • t-colorable graphs
  • Graphs and hypergraphs with bounded covering number.