Impartial Digraphs


We prove a conjecture of Fox, Huang, and Lee that characterizes directed graphs that have constant density in all tournaments: they are disjoint unions of trees that are each constructed in a certain recursive way.

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We thank the anonymous referees for careful readings and helpful comments.

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Corresponding author

Correspondence to Yufei Zhao.

Additional information

Zhao was supported by NSF Awards DMS-1362326 and DMS-1764176, the MIT Solomon Buchsbaum Fund, and a Sloan Research Fellowship. Zhou was supported by the MIT Undergraduate Research Opportunities Program.

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Zhao, Y., Zhou, Y. Impartial Digraphs. Combinatorica 40, 875–896 (2020).

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Mathematics Subject Classification (2010)

  • 05C20