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Threshold Digraphs
Brian Cloteaux1, M Drew LaMar2, Elizabeth Moseman1
1National Institute of Standards and Technology, Gaithersburg, MD 20899.
Summary
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.
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.
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