15 papers
Forbidden subposet problems in the linear lattice
Balázs Patkós, Casey Tompkins
We study weak and strong forbidden subposet problems in the linear lattice . We show that the -analogues of the Bukh--Griggs--Lu conjecture fail for every prime power $q…
Crown-free families and forbidden subposets with
Balázs Patkós, Casey Tompkins
The maximum size of a weak -free family is denoted by . Let denote the maximum integer such that the union of any consecut…
An Improved Lower Bound for Diamond-Free Families
Casey Tompkins
We construct a diamond-free family in the Boolean lattice whose size is asymptotically larger than the union of two middle layers. Denote the diamond poset by and let $La(n,Q…
A note on the extremal number of Berge-
Nika Salia, Casey Tompkins
We improve the known upper bound for the extremal number of Berge--free -uniform hypergraphs. More precisely, we prove that every -vertex -uniform hypergraph with no…
An Erdős-Ko-Rado Theorem for Tilings
Casey Tompkins
We prove an Erdős-Ko-Rado type extremal result for tilings of a chessboard by tiles whose lengths belong to a set . Two tilings are said to intersect if they contai…
An Intersection-Weighted Erdős-Ko-Rado Theorem
Casey Tompkins
We consider an Erdős-Ko-Rado type sum that weights each member of a uniform family according to its smallest intersection with the rest of the family. We prove that once the ground…
Turán-Type Extremal Results for Distance- Graphs
Zhen He, Nika Salia, Casey Tompkins +1
We study Turán-type extremal problems for distance graphs, motivated by work of Csikvári, Bollobás, Tyomkyn, and Uzzell. We determine the maximum number of vertex pairs at distance…
The number of induced paths in outerplanar graphs
Yichen Wang, Ervin Győri, Casey Tompkins +1
Let denote the path with vertices, and be the maximum number of induced copies of in an -vertex outerpla…
The Turán number of the Cartesian product of a star and an edge
Xiamiao Zhao, Xin Cheng, Cheng Chi +3
Let denote the cycle of length , be a star with edges. And let be the graph consisting of copies of sharing one fixed edge. Equivalently, $B_t=K_…
Sets avoiding a rainbow solution to the generalized Schur equation
Ervin Győri, Zhen He, Zequn Lv +4
A classical result in combinatorial number theory states that the largest subset of avoiding a solution to the equation is of size . For all intege…
Metric graphs of negative type
Rutger Campbell, Kevin Hendrey, Ben Lund +1
The negative type inequalities of a metric space are closely tied to embeddability. A result by Gupta, Newman, and Rabinovich implies that if a metric graph does not contain a…
On hypergraph Turán problems with bounded matching number
Dániel Gerbner, Casey Tompkins, Junpeng Zhou
Very recently, Alon and Frankl, and Gerbner studied the maximum number of edges in -vertex -free graphs with bounded matching number, respectively. We consider the analogous…
Connected Turán numbers for Berge paths in hypergraphs
Lin-Peng Zhang, Hajo Broersma, Ervin Győri +2
Let be a family of -uniform hypergraphs. Denote by $\ex^{\mathrm{conn}}_r(n,\mathcal{F})$ the maximum number of hyperedges in an -vertex connected -uniform h…
On graphs without cycles of length 0 modulo 4
Ervin Győri, Binlong Li, Nika Salia +3
Bollobás proved that for every and such that contains an even number, an -vertex graph containing no cycle of length can contain at…
A note on universal graphs for spanning trees
Ervin Győri, Binlong Li, Nika Salia +1
Chung and Graham considered the problem of minimizing the number of edges in an -vertex graph containing all -vertex trees as a subgraph. They showed that such a graph has at…