Book:Gary Chartrand/Introductory Graph Theory

From ProofWiki
Jump to navigation Jump to search

Gary Chartrand: Introductory Graph Theory

Published $\text {1985}$, Dover Publications, Inc.

ISBN 0-486-24775-9.

Subject Matter

Republication with corrections of Graphs as Mathematical Models from $1977$.


Chapter l: Mathematical Models
1.1 Nonmathematical Models
1.2 Mathematical Models
1.3 Graphs
1.4 Graphs as Mathematical Models
1.5 Directed Graphs as Mathematical Models
1.6 Networks as Mathematical Models
Chapter 2: Elementary Concepts of Graph Theory
2.1 The Degree of a Vertex
2.2 Isomorphic Graphs
2.3 Connected Graphs
2.4 Cut-Vertices and Bridges
Chapter 3: Transportation Problems
3.1 The Königsberg Bridge Problem: An Introduction to Eulerian Graphs
3.2 The Salesman's Problem: An Introduction to Hamiltonian Graphs
Chapter 4: Connection Problems
4.1: The Minimal Cohnector Problem: An Introduction to Trees
4.2 Trees and Probability
4.3 PERT and the Critical Path Method
Chapter 5: Party Problems
5.1 The Problem of the Eccentric Hosts: An Introduction to Ramsey Numbers
5.2 The Dancing Problem: An Introduction to Matching
Chapter 6: Games and Puzzles
6.1 The Problem of the Four Multicolored Cubes: A Solution to "Instant Insanity"
6.2 The Knight's Tour
6.3 The Tower of Hanoi
6.4 The Three Cannibals and Three Missionaries Problem
Chapter 7: Digraphs and Mathematical Models
7.1 A Traffic System Problem: An Introduction to Orientable Graphs
7.2 Tournaments
7.3 Paired Comparisons and How to Fix Elections
Chapter 8: Graphs and Social Psychology
8.1 The Problem of Balance
8.2 The Problem of Clustering
8.3 Graphs and Transactional Analysis
Chapter 9
Planar Graphs and Coloring Problems
9.1 The Three Houses and Three Utilities Problem: An Introduction to Planar Graphs
9.2 A Scheduling Problem: An Introduction to Chromatic Numbers
9.3 The Four Color Problem
Chapter 10: Graphs and Other Mathematics
10.1 Graphs and Matrices
10.2 Graphs and Topology
10.3 Graphs and Groups
Appendix: Sets, Relations, Functions, Proofs
A.1 Sets and Subsets
A.2 Cartesian Products and Relations
A.3 Equivalence Relations
A.4 Functions
A.5 Theorems and Proofs
A.6 Mathematical Induction
Answers, Hints, and Solutions to Selected Exercises


Source work progress