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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

classification math.CO
keywords vertexconstructionextremalinducibilityreplacedsourcetournamenttournaments
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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 4 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.

  3. The semi-inducibility problem

    math.CO 2025-01 accept novelty 7.0 of 10

    The authors determine sharp or almost sharp maximum densities for alternating walks and cycles and for every 4-cycle colour pattern in red-blue complete graphs, and exhibit a positive-coefficient quantum graph whose o...

  4. Forcing Quasirandomness in a Regular Tournament

    math.CO 2025-01 conditional novelty 6.0 of 10

    All tournaments on at most five vertices that force quasirandomness in nearly regular tournaments are classified: eleven force it and nine do not.

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