Advanced graph theory and combinatorics / Michel Rigo.

Format:

Book

Author/Creator:

Rigo, Michel, author.

Series:

Computer engineering series (London, England)

Computer Engineering Series

Language:

English

Subjects (All):

Graph theory.

Combinatorial analysis.

Physical Description:

1 online resource : illustrations.

Edition:

1st ed.

Place of Publication:

London, England ; Hoboken, New Jersey : ISTE : Wiley, 2016.

Summary:

Advanced Graph Theory focuses on some of the main notions arising in graph theory with an emphasis from the very start of the book on the possible applications of the theory and the fruitful links existing with linear algebra. The second part of the book covers basic material related to linear recurrence relations with application to counting and the asymptotic estimate of the rate of growth of a sequence satisfying a recurrence relation.

Contents:

Intro

Table of Contents

Dedication

Title

Copyright

Foreword

Introduction

1 A First Encounter with Graphs

1.1. A few definitions

1.2. Paths and connected components

1.3. Eulerian graphs

1.4. Defining Hamiltonian graphs

1.5. Distance and shortest path

1.6. A few applications

1.7. Comments

1.8. Exercises

2 A Glimpse at Complexity Theory

2.1. Some complexity classes

2.2. Polynomial reductions

2.3. More hard problems in graph theory

3 Hamiltonian Graphs

3.1. A necessary condition

3.2. A theorem of Dirac

3.3. A theorem of Ore and the closure of a graph

3.4. Chvátal's condition on degrees

3.5. Partition of Kn into Hamiltonian circuits

3.6. De Bruijn graphs and magic tricks

3.7. Exercises

4 Topological Sort and Graph Traversals

4.1. Trees

4.2. Acyclic graphs

4.3. Exercises

5 Building New Graphs from Old Ones

5.1. Some natural transformations

5.2. Products

5.3. Quotients

5.4. Counting spanning trees

5.5. Unraveling

5.6. Exercises

6 Planar Graphs

6.1. Formal definitions

6.2. Euler's formula

6.3. Steinitz' theorem

6.4. About the four-color theorem

6.5. The five-color theorem

6.6. From Kuratowski's theorem to minors

6.7. Exercises

7 Colorings

7.1. Homomorphisms of graphs

7.2. A digression: isomorphisms and labeled vertices

7.3. Link with colorings

7.4. Chromatic number and chromatic polynomial

7.5. Ramsey numbers

7.6. Exercises

8 Algebraic Graph Theory

8.1. Prerequisites

8.2. Adjacency matrix

8.3. Playing with linear recurrences

8.4. Interpretation of the coefficients

8.5. A theorem of Hoffman

8.6. Counting directed spanning trees

8.7. Comments

8.8. Exercises

9 Perron-Frobenius Theory

9.1. Primitive graphs and Perron's theorem

9.2. Irreducible graphs.

9.3. Applications

9.4. Asymptotic properties

9.5. The case of polynomial growth

9.6. Exercises

10 Google's Page Rank

10.1. Defining the Google matrix

10.2. Harvesting the primitivity of the Google matrix

10.3. Computation

10.4. Probabilistic interpretation

10.5. Dependence on the parameter α

10.6. Comments

Bibliography

Index

End User Licence Agreement.

Notes:

Includes bibliographical references and index.

Description based on print version record.

ISBN:

9781119058649

1119058643

9781119058618

1119058619

9781119008989

1119008980

OCLC:

964526286