Erdös on Graphs

His Legacy of Unsolved Problems

The list of content:

• Preface
  Remembering Uncle Paul
• Chapter 1: Introduction
  1.1. Definitions and notations
  1.2 About the references
  
• Chapter 2: Ramsey theory
  2.1. Introduction
  2.2. Origins
  2.3. Classical Ramsey theory
  2.4. Graph Ramsey theory
  2.5. Multi-colored Ramsey numbers
  2.6. Size Ramsey numbers
  2.7. Induced Ramsey numbers
  2.8. Ramsey theory for hypergraphs
  
• Chapter 3: Extremal graph theory
  3.1. Introduction
  3.2. Origins
  3.3. Tur'an numbers for bipartite graphs
  3.4. Tur'an problems for even cycles and their generalizations
  3.5. General extremal problems
• Chapter 4: Coloring, packing and covering
  4.1. Introduction
  4.2. Origins
  4.3. Chromatic number and girth
  4.4. Chromatic number and cliques
  4.5. List colorings
  4.6. Critical graphs
  4.7. Chromatic index
  4.8. General coloring problems
  4.9. Covering and packing
• Chapter 5: Random graphs and graph enumeration
  5.1. Introduction
  5.2. Origins
  5.3. The chromatic number of a random graph
  5.4. General problems on random graphs
  5.5. Subgraph enumeration
• Chapter 6: Hypergraphs
  6.1. Introduction
  6.2. Origins
  6.3. Tur'an problems for hypergraphs
  6.4. Stars
  6.5. a problem of Erd"os, Faber and Lov'asz
  6.6. Chromatic hypergraphs
  6.7. General hypergraph problems
• Chapter 7: Infinite graphs
  7.1. Origins
  7.2. Introduction
  7.3. Ordinary partition relations for ordinals
  7.4. Chromatic numbers and infinite graphs
  7.5. General problems for infinite graphs
• Erd"os stories as told by Andy V'azsonyi
  Paul Erd"os, The world's most beloved mathematical genius "leaves"
  Erd"os, cars and goats, and Bayes' theorem
  Erd"os, the other woman and the theorem of penta chords
• Index