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A class of perfect graphs in genetics

A Thomas1

  • 1School of Mathematical Sciences, University of Bath, UK.

IMA Journal of Mathematics Applied in Medicine and Biology
|January 1, 1993
PubMed
Summary

Genealogy graphs are simplified using male-female links to resolve cycles. This method results in a perfect graph representation for family trees.

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Area of Science:

  • Graph theory
  • Computational biology
  • Genetics

Background:

  • Genealogical data is often complex and challenging to represent graphically.
  • Traditional methods may struggle with cyclical relationships inherent in family structures.

Purpose of the Study:

  • To develop a simplified and regularized graphical representation of genealogies.
  • To investigate the properties of graphs derived from genealogical data using specific link types.

Main Methods:

  • Utilizing only male-female links to represent relationships.
  • Applying a chording technique to regularize cycles within the genealogical graph.
  • Analyzing the structural properties of the resulting graph.

Main Results:

  • The graphical representation of genealogies is effectively regularized by chording cycles.
  • The resulting graph demonstrates perfect graph properties.
  • This method provides a clear and structured visualization of family relationships.

Conclusions:

  • The chording of cycles using male-female links offers a robust method for representing genealogies.
  • The perfect graph property simplifies complex family structures for analysis.
  • This approach has implications for genetic studies and family history research.

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