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Advanced Graph Theory and Combinatorics 1st Edition by Michel Rigo 1119058643 9781119058649

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Advanced Graph Theory and Combinatorics 1st Edition Michel Rigo Digital Instant Download

Author(s): Michel Rigo
ISBN(s): 9781848216167, 1848216165
Edition: 1
File Details: PDF, 1.23 MB
Year: 2016
Language: english
SKU: EB-6746768 Category: Tag:

Advanced Graph Theory and Combinatorics 1st Edition by Michel Rigo – Ebook PDF Instant Download/Delivery: 1119058643, 978-1119058649
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Product details:

ISBN 10:         1119058643
ISBN 13: 978-1119058649
Author:          Michel Rigo

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.
 

Advanced Graph Theory and Combinatorics 1st Table of contents:

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
  •  

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