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Threshold Digraphs.

Brian Cloteaux1, M Drew LaMar2, Elizabeth Moseman1

  • 1National Institute of Standards and Technology, Gaithersburg, MD 20899.

Journal of Research of the National Institute of Standards and Technology
|November 25, 2015
PubMed
Summary
This summary is machine-generated.

This study defines threshold digraphs based on unique degree sequences. We present equivalent characterizations of these digraphs, leading to a concise proof of the Fulkerson-Chen theorem for general digraphs.

Keywords:
Fulkerson-Chen theoremdigraph realizationsthreshold digraphs

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Area of Science:

  • Graph theory
  • Discrete mathematics
  • Combinatorics

Background:

  • Threshold digraphs are defined by unique vertex labeled realizations of their degree sequences.
  • Understanding these unique properties is crucial for graph theory research.

Purpose of the Study:

  • To present and demonstrate the equivalence of several characterizations for threshold digraphs and their degree sequences.
  • To provide a new, simplified proof of the Fulkerson-Chen theorem.

Main Methods:

  • Characterization of threshold digraphs.
  • Analysis of degree sequences.
  • Proof techniques in graph theory.

Main Results:

  • Several equivalent characterizations of threshold digraphs and their degree sequences were established.
  • A novel and concise proof of the Fulkerson-Chen theorem was derived.

Conclusions:

  • The established characterizations offer a deeper understanding of threshold digraphs.
  • The new proof simplifies and validates the Fulkerson-Chen theorem for general digraphs.