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 -