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Combinatorics and Graph Theory

Combinatorics is often described briefly as being about counting, and indeed counting is a large part of combinatorics.Graph theory is concerned with various types of networks, or really models of networks called graphs. These are not the graphs of analytic geometry, but what are often described as "points connected by lines''.

Combinatorics and Discrete MathematicsMathematics
Author
David Guichard
Publisher
Whitman College
Source
LibreTexts
License
CC BY-NC-SA
Language
EN
Category
Basic Sciences
Read online Download PDF (open licence)
Contents· 50 sections
  1. 01: Fundamentals
  2. 1.01: Prelude to Fundamentals
  3. 1.02: Examples
  4. 1.03: Combinations and Permutations
  5. 1.04: Binomial Coefficients
  6. 1.05: Bell Numbers
  7. 1.06: Choice with Repetition
  8. 1.07: The Pigeonhole Principle
  9. 1.08: Sperner's Theorem
  10. 1.09: Stirling numbers
  11. 1.E: Fundamentals (Exercises)
  12. 02: Inclusion-Exclusion
  13. 2.01: The Inclusion-Exclusion Formula
  14. 2.02: Forbidden Position Permutations
  15. 2.E: Inclusion-Exclusion (Exercises)
  16. 03: Generating Functions
  17. 3.01: Prelude to Generating Functions
  18. 3.02: Newton's Binomial Theorem
  19. 3.03: Exponential Generating Functions
  20. 3.04: Partitions of Integers
  21. 3.05: Recurrence Relations
  22. 3.06: Catalan Numbers
  23. 3.E: Generating Functions (Exercises)
  24. 04: Systems of Distinct Representatives
  25. 4.01: Prelude to Systems of Distinct Representatives
  26. 4.02: Existence of SDRs
  27. 4.03: Partial SDRs
  28. 4.04: Latin Squares
  29. 4.05: Introduction to Graph Theory
  30. 4.06: Matchings
  31. 4.E: Systems of Distinct Representatives (Exercises)
  32. 05: Graph Theory
  33. 5.01: The Basics of Graph Theory
  34. 5.02: Euler Circuits and Walks
  35. 5.03: Hamilton Cycles and Paths
  36. 5.04: Bipartite Graphs
  37. 5.05: Trees
  38. 5.06: Optimal Spanning Trees
  39. 5.07: Connectivity
  40. 5.08: Graph Coloring
  41. 5.09: The Chromatic Polynomial
  42. 5.10: Coloring Planar Graphs
  43. 5.11: Directed Graphs
  44. 5.E: Graph Theory (Exercises)
  45. 06: PolyaRedfield Counting
  46. 6.01: Prelude to Pólya–Redfield Counting
  47. 6.02: Groups of Symmetries
  48. 6.03: Burnside's Theorem
  49. 6.04: Pólya-Redfield Counting
  50. 6.E: Pólya–Redfield Counting (Exercises)