TY - JOUR

T1 - Turán numbers of general star forests in hypergraphs

AU - Zhang, Lin Peng

AU - Broersma, Hajo

AU - Wang, Ligong

N1 - Publisher Copyright:
© 2024 The Author(s)

PY - 2025/1

Y1 - 2025/1

N2 - 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.

AB - 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.

KW - UT-Hybrid-D

KW - Star forest

KW - Turán number

KW - Berge hypergraph

UR - http://www.scopus.com/inward/record.url?scp=85201276557&partnerID=8YFLogxK

U2 - 10.1016/j.disc.2024.114219

DO - 10.1016/j.disc.2024.114219

M3 - Article

AN - SCOPUS:85201276557

SN - 0012-365X

VL - 348

JO - Discrete mathematics

JF - Discrete mathematics

IS - 1

M1 - 114219

ER -