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December 2018 Erdős-Rényi theory for asymmetric digraphs
Shohei Satake, Masanori Sawa, Masakazu Jimbo
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SUT J. Math. 54(2): 109-129 (December 2018). DOI: 10.55937/sut/1547570388


We introduce the concept of the asymmetry number for finite digraphs, as a natural generalization of that for undirected graphs by Erdős and Rényi in 1963. We prove an upper bound for the asymmetry number of finite digraphs and give a condition for equality. We show that our bound is asymptotically best for digraphs with sufficiently large order. We also consider the random oriented graph RO, and make some remarks on Aut(RO).

Funding Statement

This research is supported by Grant-in-Aid for JSPS Fellows 18J11282, Grant-in-Aid for Young Scientists (B) 26870259 and Grant-in-Aid for Scientific Research (B) 15H03636 of the Japan Society for the Promotion of Science.


We would appreciate Hikoe Enomoto and Masatake Hirao for valuable comments and suggestions. The authors would also like to thank Peter J. Cameron for his careful reading of our paper.


Download Citation

Shohei Satake. Masanori Sawa. Masakazu Jimbo. "Erdős-Rényi theory for asymmetric digraphs." SUT J. Math. 54 (2) 109 - 129, December 2018.


Received: 21 July 2017; Revised: 10 July 2018; Published: December 2018
First available in Project Euclid: 8 June 2022

Digital Object Identifier: 10.55937/sut/1547570388

Primary: 05C20‎ , 05C80

Keywords: acyclic random oriented graph , Asymmetry number , random digraphs , random oriented graph

Rights: Copyright © 2018 Tokyo University of Science

Vol.54 • No. 2 • December 2018
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