Turán numbers of general star forests in hypergraphs

Lin Peng Zhang, Hajo Broersma*, Ligong Wang

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

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Abstract

Let F be a family of r-uniform hypergraphs, and let H be an r-uniform hypergraph. Then H is called F-free if it does not contain any member of F as a subhypergraph. The Turán number of F, denoted by exr(n,F), is the maximum number of hyperedges in an F-free n-vertex r-uniform hypergraph. Our current results are motivated by earlier results on Turán numbers of star forests and hypergraph star forests. In particular, Lidický et al. (2013) [17] determined the Turán number ex(n,F) of a star forest F for sufficiently large n. Recently, Khormali and Palmer (2022) [13] generalized the above result to three different well-studied hypergraph settings (the expansions of a graph, linear hypergraphs and Berge hypergraphs), but restricted to the case that all stars in the hypergraph star forests are identical. We further generalize these results to general star forests in hypergraphs.

Original languageEnglish
Article number114219
Number of pages14
JournalDiscrete mathematics
Volume348
Issue number1
DOIs
Publication statusPublished - Jan 2025

Keywords

  • UT-Hybrid-D
  • Star forest
  • Turán number
  • Berge hypergraph

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