Combinatorics and Graph Theory

Name: Combinatorics and Graph Theory
Availability: InStock
ISBN: 9780387797106

ISBN-10: 0387797106

ISBN-13: 9780387797106

Edition: 2nd 2008

Authors: John M. Harris, Jeffry L. Hirst, Michael J. Mossinghoff

List price: $54.95

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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.

Book details

List price: $54.95
Edition: 2nd
Copyright year: 2008
Publisher: Springer New York
Publication date: 9/19/2008
Binding: Hardcover
Pages: 381
Size: 6.10" wide x 9.25" long x 0.75" tall
Weight: 1.804
Language: English



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