Work

Turán numbers of general star forests in hypergraphs

Year: 2024

Type: article

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.

Source: Discrete Mathematics

DOI: 10.1016/j.disc.2024.114219

Authors: Lin-Peng Zhang, Hajo Broersma, Ligong Wang

Language: English

Topic: Limits and Structures in Graph Theory

Subfield: Discrete Mathematics and Combinatorics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,120

Funders: National Natural Science Foundation of China, China Scholarship Council

Awards: G1429975565, G867893535