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Inducibility of 4-vertex tournaments

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arxiv 2103.07047 v2 pith:BYGRXTGG submitted 2021-03-12 math.CO

Dalton Burke , Bernard Lidický , Florian Pfender , Michael Phillips This is my paper · ORCID
classification math.CO
keywords vertexconstructionextremalinducibilityreplacedsourcetournamenttournaments
verification ladder T0 review T1 audit T2 compute T3 formal
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abstract

We determine the inducibility of all tournaments with at most $4$ vertices together with the extremal constructions. The $4$-vertex tournament containing an oriented $C_3$ and one source vertex has a particularly interesting extremal construction. It is an unbalanced blow-up of an edge, where the sink vertex is replaced by a quasi-random tournament and the source vertex is iteratively replaced by a copy of the construction itself.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Maximizing directed cycles in tournaments

    math.CO 2026-08 conditional novelty 8.0 of 10

    For tournaments on n vertices, the maximum number of directed 4k-cycles is asymptotic to (1 + 2 times the sum from i=1 to infinity of (2/((2i-1)pi))^(4k)) times the random tournament's count, attained by the carousel ...

  2. Generalized Tur\'an problem for directed cycles

    math.CO 2025-05 conditional novelty 7.0 of 10

    The maximum number of directed k-cycles in an n-vertex oriented graph with no directed l-cycle is Theta(n^k) when k does not divide l, Theta(n^(k-1)) when k divides l, and the leading constant is determined for large l.

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