2023/06/13 by Lin-Peng Zhang, Hajo Broersma, Zhang, Lin-Peng +3
Mathematics · Computer Science · #Limits and Structures in Graph Theory #Advanced Graph Theory Research
paper · pdf · doi:10.48550/arxiv.2306.12463
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, Liu and Palmer [Electron. J. Combin. 20 (2013)] determined the Turán number ex(n,F) of a star forest F for sufficiently large n. Recently, Khormali and Palmer [European. J. Combin. 102 (2022) 103506] generalized the above result to three different well-studied hypergraph settings, but restricted to the case that all stars in the hypergraph star forests are identical. We further generalize these results to general hypergraph star forests.