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Quasi-random graphs.

F R Chung1, R L Graham, R M Wilson

  • 1Bell Communications Research, Morristown, NJ 07960.

Proceedings of the National Academy of Sciences of the United States of America
|February 1, 1988
PubMed
Summary
This summary is machine-generated.

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We identified a large group of graph properties common to random graphs. Verifying these graph properties in specific graph families is often simpler than with random graphs.

Area of Science:

  • Graph theory
  • Theoretical computer science

Background:

  • Random graphs are a fundamental concept in graph theory.
  • Identifying shared properties among graph families is computationally challenging.

Purpose of the Study:

  • To introduce a novel equivalence class of graph properties.
  • To demonstrate that these properties are shared by random graphs.
  • To provide a more tractable method for verifying graph properties.

Main Methods:

  • Introduction of a new class of graph properties.
  • Theoretical analysis of property inheritance in graph families.
  • Comparative study of verification complexity between random graphs and specific families.

Main Results:

Related Experiment Videos

  • A large equivalence class of graph properties is formally defined.
  • All properties within this class are demonstrated to be shared by random graphs.
  • Verification of these properties in specific graph families is shown to be computationally easier.

    • Conclusions:

    • The newly defined equivalence class offers a structured way to understand graph properties.
    • This class provides a practical alternative to analyzing random graphs for certain properties.
    • The findings simplify the verification process for specific graph families.