Combinatorics and Graph Theory

ISBN-10: 0387797106
ISBN-13: 9780387797106
Edition: 2nd 2008
List price: $54.95 Buy it from $28.23
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Description: This book covers a wide variety of topics in combinatorics and graph theory. It includes results and problems that cross subdisciplines, emphasizing relationships between different areas of mathematics.

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Book details

List price: $54.95
Edition: 2nd
Copyright year: 2008
Publisher: Springer
Publication date: 9/19/2008
Binding: Hardcover
Pages: 381
Size: 6.75" wide x 9.75" long x 0.75" tall
Weight: 1.496
Language: English

This book covers a wide variety of topics in combinatorics and graph theory. It includes results and problems that cross subdisciplines, emphasizing relationships between different areas of mathematics.

Preface to the Second Edition
Preface to the First Edition
Graph Theory
Introductory Concepts
Graphs and Their Relatives
The Basics
Special Types of Graphs
Distance in Graphs
Definitions and a Few Properties
Graphs and Matrices
Graph Models and Distance
Trees
Definitions and Examples
Properties of Trees
Spanning Trees
Counting Trees
Trails, Circuits, Paths, and Cycles
The Bridges of Konigsberg
Eulerian Trails and Circuits
Hamiltonian Paths and Cycles
Three Open Problems
Planarity
Definitions and Examples
Euler's Formula and Beyond
Regular Polyhedra
Kuratowski's Theorem
Colorings
Definitions
Bounds on Chromatic Number
The Four Color Problem
Chromatic Polynomials
Matchings
Definitions
Hall's Theorem and SDRs
The Konig-Egervary Theorem
Perfect Matchings
Ramsey Theory
Classical Ramsey Numbers
Exact Ramsey Numbers and Bounds
Graph Ramsey Theory
References
Combinatorics
Some Essential Problems
Binomial Coefficients
Multinomial Coefficients
The Pigeonhole Principle
The Principle of Inclusion and Exclusion
Generating Functions
Double Decks
Counting with Repetition
Changing Money
Fibonacci Numbers
Recurrence Relations
Catalan Numbers
Polya's Theory of Counting
Permutation Groups
Burnside's Lemma
The Cycle Index
Polya's Enumeration Formula
de Bruijn's Generalization
More Numbers
Partitions
Stirling Cycle Numbers
Stirling Set Numbers
Bell Numbers
Eulerian Numbers
Stable Marriage
The Gale-Shapley Algorithm
Variations on Stable Marriage
Combinatorial Geometry
Sylvester's Problem
Convex Polygons
References
Infinite Combinatorics and Graphs
Pigeons and Trees
Ramsey Revisited
ZFC
Language and Logical Axioms
Proper Axioms
Axiom of Choice
The Return of der Konig
Ordinals, Cardinals, and Many Pigeons
Cardinality
Ordinals and Cardinals
Pigeons Finished Off
Incompleteness and Cardinals
Godel's Theorems for PA and ZFC
Inaccessible Cardinals
A Small Collage of Large Cardinals
Weakly Compact Cardinals
Infinite Marriage Problems
Hall and Hall
Countably Many Men
Uncountably Many Men
Espousable Cardinals
Perfect Matchings
Finite Combinatorics with Infinite Consequences
k-critical Linear Orderings
Points of Departure
References
References
Index

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