6 papers · 1 filter
Rainbow Turán problems for a matching and any other graph
Dániel Gerbner, Shujing Miao
For a family of graphs $\cF$, a graph is called $\cF$-free if it does not contain any member of $\cF$ as a subgraph. Given a collection of graphs on the same ver…
On degree powers and counting stars in -free graphs
Dániel Gerbner
Given a positive integer and a graph with degree sequence , we define . We let be the largest value of $e_r(G…
On forbidding graphs as traces of hypergraphs
Dániel Gerbner, Michael E. Picollelli
We say that a hypergraph contains a graph as a trace if there exists some set such that $\mathcal{H}|_S=\{h\cap S: h\in E(\mathcal{H})\}…
On non-degenerate Turán problems for expansions
Dániel Gerbner
The -uniform expansion of a graph is obtained by enlarging each edge with new vertices such that altogether we use new vertices. Two simple lo…
On Turán problems with bounded matching number
Dániel Gerbner
Very recently, Alon and Frankl initiated the study of the maximum number of edges in -vertex -free graphs with matching number at most . For fixed and , we determin…
Uniquely -saturated graphs
Yuying Li, Kexiang Xu, Dániel Gerbner +1
A graph is uniquely -saturated if it contains no copy of a graph as a subgraph, but adding any new edge into creates exactly one copy of . Let be the…