Preface to the Second Edition |
Preface to the First Edition |
Graph Theory / 1: |
Introductory Concepts / 1.1: |
Graphs and Their Relatives / 1.1.1: |
The Basics / 1.1.2: |
Special Types of Graphs / 1.1.3: |
Distance in Graphs / 1.2: |
Definitions and a Few Properties / 1.2.1: |
Graphs and Matrices / 1.2.2: |
Graph Models and Distance / 1.2.3: |
Trees / 1.3: |
Definitions and Examples / 1.3.1: |
Properties of Trees / 1.3.2: |
Spanning Trees / 1.3.3: |
Counting Trees / 1.3.4: |
Trails, Circuits, Paths, and Cycles / 1.4: |
The Bridges of Konigsberg / 1.4.1: |
Eulerian Trails and Circuits / 1.4.2: |
Hamiltonian Paths and Cycles / 1.4.3: |
Three Open Problems / 1.4.4: |
Planarity / 1.5: |
Euler's Formula and Beyond / 1.5.1: |
Regular Polyhedra / 1.5.3: |
Kuratowski's Theorem / 1.5.4: |
Colorings / 1.6: |
Definitions / 1.6.1: |
Bounds on Chromatic Number / 1.6.2: |
The Four Color Problem / 1.6.3: |
Chromatic Polynomials / 1.6.4: |
Matchings / 1.7: |
Hall's Theorem and SDRs / 1.7.1: |
The Konig-Egervary Theorem / 1.7.3: |
Perfect Matchings / 1.7.4: |
Ramsey Theory / 1.8: |
Classical Ramsey Numbers / 1.8.1: |
Exact Ramsey Numbers and Bounds / 1.8.2: |
Graph Ramsey Theory / 1.8.3: |
References / 1.9: |
Combinatorics / 2: |
Some Essential Problems / 2.1: |
Binomial Coefficients / 2.2: |
Multinomial Coefficients / 2.3: |
The Pigeonhole Principle / 2.4: |
The Principle of Inclusion and Exclusion / 2.5: |
Generating Functions / 2.6: |
Double Decks / 2.6.1: |
Counting with Repetition / 2.6.2: |
Changing Money / 2.6.3: |
Fibonacci Numbers / 2.6.4: |
Recurrence Relations / 2.6.5: |
Catalan Numbers / 2.6.6: |
Polya's Theory of Counting / 2.7: |
Permutation Groups / 2.7.1: |
Burnside's Lemma / 2.7.2: |
The Cycle Index / 2.7.3: |
Polya's Enumeration Formula / 2.7.4: |
de Bruijn's Generalization / 2.7.5: |
More Numbers / 2.8: |
Partitions / 2.8.1: |
Stirling Cycle Numbers / 2.8.2: |
Stirling Set Numbers / 2.8.3: |
Bell Numbers / 2.8.4: |
Eulerian Numbers / 2.8.5: |
Stable Marriage / 2.9: |
The Gale-Shapley Algorithm / 2.9.1: |
Variations on Stable Marriage / 2.9.2: |
Combinatorial Geometry / 2.10: |
Sylvester's Problem / 2.10.1: |
Convex Polygons / 2.10.2: |
Infinite Combinatorics and Graphs / 2.11: |
Pigeons and Trees / 3.1: |
Ramsey Revisited / 3.2: |
ZFC / 3.3: |
Language and Logical Axioms / 3.3.1: |
Proper Axioms / 3.3.2: |
Axiom of Choice / 3.3.3: |
The Return of der Konig / 3.4: |
Ordinals, Cardinals, and Many Pigeons / 3.5: |
Cardinality / 3.5.1: |
Ordinals and Cardinals / 3.5.2: |
Pigeons Finished Off / 3.5.3: |
Incompleteness and Cardinals / 3.6: |
Godel's Theorems for PA and ZFC / 3.6.1: |
Inaccessible Cardinals / 3.6.2: |
A Small Collage of Large Cardinals / 3.6.3: |
Weakly Compact Cardinals / 3.7: |
Infinite Marriage Problems / 3.8: |
Hall and Hall / 3.8.1: |
Countably Many Men / 3.8.2: |
Uncountably Many Men / 3.8.3: |
Espousable Cardinals / 3.8.4: |
Finite Combinatorics with Infinite Consequences / 3.8.5: |
k-critical Linear Orderings / 3.10: |
Points of Departure / 3.11: |
Index / 3.12: |
Preface to the Second Edition |
Preface to the First Edition |
Graph Theory / 1: |