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arXiv · 1312.1205

A Note on the Inducibility of 4-vertex Graphs

Chaim Even-Zohar·Nati Linial
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Abstract

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| -> infinity. Already for 4-vertex graphs many questions are still open. Thus, the inducibility of the 4-path was addressed in a construction of Exoo (1986), but remains unknown. Refuting a conjecture of Erdos, Thomason (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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Chaim Even-Zohar, Nati Linial. 2014-10-21. A Note on the Inducibility of 4-vertex Graphs. https://doi.org/10.1007/s00373-014-1475-4

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