On the number of 4-cycles in a tournament

Linial, Nathan; Morgenstern, Avraham

doi:10.48550/arxiv.1405.1576

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2014

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“…Indeed, there is substantial recent activity in this domain [20,19,22], and additional combinatorial structures with natural notions of local profile and inducibility are being investigated as well, e.g. tournaments [23] trees [4], and permutations [35].…”

Section: Introductionmentioning

confidence: 99%

A Note on the Inducibility of $$4$$ 4 -Vertex Graphs

Even-Zohar

Linial

2014

Graphs and Combinatorics

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There is much recent interest in understanding the density at which constant size graphs can appear in a very large graph. Specifically, the inducibility of a graph H is its extremal density, as an induced subgraph of G, where |G| → ∞. Already for 4-vertex graphs many questions are still open. Thus, the inducibility of the 4-path was addressed in a construction of Exoo (Ars Combin 22:5-10, 1986), but remains unknown. Refuting a conjecture of Erdős, Thomason (Combinatorica 17(1):125-134, 1997) constructed graphs with a small density of both 4-cliques and 4-anticliques. In this note, we merge these two approaches and construct better graphs for both problems.

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