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Fundamentals of Graph Theory, by A.A. Zykov

An English translation, assisted by the author, of the 1987 Russian edition (M.:Nauka.Gl.red.Fiz.-mat.lit.). Includes a Glossary-Index-Bibliography that should be of immense value. Many exercises at the end of each section. A sample of topics: Simple, labeled, multi-, topological and directed graphs; numerous invariants - optimum and critical graphs; the isomorphism problem and Vizing's construction; reconstruction problems; matchings; embeddings in surfaces; planarity; Hadwiger's conjecture; various colorings; perfect graphs; reachability; kernels; many others. Appendix on Boolean methods in graph theory.

TABLE OF CONTENTS

1. FROM THE AUTHOR
   
2. INTRODUCTION
   
3. CHAPTER 1. IDENTIFICATION
   
   1. Simple Graphs
      
   2. Isomorphism
      
   3. Invariants
      
   4. Calculation of Invariants
      
   5. The Isomorphism Problem
      
   6. Some Applications of Density and Nondensity
      
   7. Algorithms for Density, Nondensity and Isomorphism
      
   8. Bounds for Density and Nondensity, Turan's Graph
      
   9. Optimum and Critical Graphs
      
   10. Reconstruction Problems
       
4. CHAPTER 2. CONNECTIVITY
   
   1. Walks
      
   2. Blocks
      
   3. Trees
      
   4. Matchings and Bipartite Graphs
      
   5. l-connected Graphs
      
   6. Labeled Graphs and Metrics
      
   7. Multigraphs
      
   8. Eulerian Chains and Cycles
      
   9. Edge Colorings
      
5. CHAPTER 3. CYCLOMATICS
   
   1. Frameworks and Cutsets
      
   2. The Space of Partials
      
   3. Incidence, Cutset, and Cycle Matrices
      
   4. Graphs with given Cutsets and Cycles
      
   5. Topological Graphs
      
   6. Planarity
      
   7. The Crusade against Crossings
      
   8. Hadwiger's Conjecture
      
   9. Colorings Plane Triangulation's
      
   10. Perfect Graphs
       
6. CHAPTER 4. ORIENTATION
   
   1. Finite Graphs of General Type
      
   2. Reachability
      
   3. Kernels
      
   4. Orientability
      
   5. Transitability
      
7. APPENDIX
   
   1. Boolean Methods in Graph Theory
      
8. CONCLUSION
   
9. GLOSSARY
   

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