8 papers
Strong Majority Edge-Coloring
Sylwia Antoniuk, Magdalena Prorok, Nika Salia
A strong majority edge-coloring of a graph is an edge-coloring in which, for every edge and every color , at most half of the edges adjacent to have color . Such a co…
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…
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 dista…
The Connected Bipartite Turán Problem for Long Cycles and Paths
Zhen He, Nika Salia, Xiutao Zhu
Caro, Patkós, and Tuza initiated a systematic study of the bipartite Turán number for trees, and in particular asked for the extremal number of edges in connected bipartite graph…
Sets avoiding a rainbow solution to the generalized Schur equation
Ervin GyÅri, 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…
Intersecting families of polynomials over finite fields
Nika Salia, Dávid Tóth
This paper establishes an analog of the ErdÅs-Ko-Rado theorem to polynomial rings over finite fields, affirmatively answering a conjecture of C. Tompkins. A -uniform family of…