A Note on the Inducibility of 4-Vertex Graphs

Chaim Even-Zohar*, Nati Linial

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

23 Scopus citations


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.

Original languageAmerican English
Pages (from-to)1367-1380
Number of pages14
JournalGraphs and Combinatorics
Issue number5
StatePublished - 24 Sep 2015

Bibliographical note

Publisher Copyright:
© 2014, Springer Japan.


  • Graph density
  • Inducibility
  • Ramsey multiplicity


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