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Extra pearls in graph theory

Anton Petrunin

Abstract

This is a supplement for "Pearls in graph theory" -- a textbook written by Nora Hartsfield and Gerhard Ringel. We discuss the following topics: Ramsey theory, Probabilistic method, Deletion-contraction formulas, Matrix theorem, Graph-polynomials, Generating functions, Minimum spanning trees, Marriage theorem and its relatives, Toroidal graphs, Rado graph, Rewriting systems.

Extra pearls in graph theory

Abstract

This is a supplement for "Pearls in graph theory" -- a textbook written by Nora Hartsfield and Gerhard Ringel. We discuss the following topics: Ramsey theory, Probabilistic method, Deletion-contraction formulas, Matrix theorem, Graph-polynomials, Generating functions, Minimum spanning trees, Marriage theorem and its relatives, Toroidal graphs, Rado graph, Rewriting systems.

Paper Structure

This paper contains 79 sections, 201 equations, 52 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Terminology
  3. Wolf, goat, and cabbage
  4. Ramsey numbers
  5. Ramsey numbers
  6. Binomial coefficients
  7. Upper bound
  8. Lower bound
  9. Probabilistic method
  10. Markov's inequality
  11. Probabilistic method
  12. Counting proof
  13. Graph of $\bm{n}$-cube
  14. Remarks
  15. Deletion and contraction
  16. ...and 64 more sections

Figures (52)

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  • ...and 47 more figures