7 citations · 28 across the 34 of their papers we have counts for
43 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 distance…
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 graphs…
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…
Intersecting families of polynomials over finite fields
Nika Salia, Dávid Tóth
This paper establishes an analog of the Erdős-Ko-Rado theorem to polynomial rings over finite fields, affirmatively answering a conjecture of C. Tompkins. A -uniform family of s…
Hypergraph saturation for the bow tie
Stijn Cambie, Nika Salia
Erdős and Sós initiated the study of the maximum size of a -uniform set system, for , with no singleton intersections years ago. In this work, we investigate the…
Saturated Partial Embeddings of Planar Graphs
Alexander Clifton, Nika Salia
In this work, we study how far one can deviate from optimal behavior when embedding a planar graph. For a planar graph , we say that a plane subgraph is a \textit…
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…
On the Small Quasi-kernel conjecture
Péter L. Erdős, Ervin Győri, Tamás Róbert Mezei +2
An independent vertex subset of the directed graph is a kernel if the set of out-neighbors of is . An independent vertex subset of is a quasi-k…
How connectivity affects the extremal number of trees
Suyun Jiang, Hong Liu, Nika Salia
The Erdős-Sós conjecture states that the maximum number of edges in an -vertex graph without a given -vertex tree is at most . Despite significant interest…
The maximum Wiener index of a uniform hypergraph
Stijn Cambie, Ervin Győri, Nika Salia +2
The Wiener index of a (hyper)graph is calculated by summing up the distances between all pairs of vertices. We determine the maximum possible Wiener index of a connected -vertex…
The maximum number of cliques in graphs with bounded odd circumference
Zequn Lv, Ervin Győri, Zhen He +3
In this work, we give the sharp upper bound for the number of cliques in graphs with bounded odd circumferences. This generalized Turán-type result is an extension of the celebrate…
Linear three-uniform hypergraphs with no Berge path of given length
Ervin Győri, Nika Salia
Extensions of Erdős-Gallai Theorem for general hypergraphs are well studied. In this work, we prove the extension of Erdős-Gallai Theorem for linear hypergraphs. In particular, we…
Set systems without a simplex, Helly hypergraphs and union-efficient families
Stijn Cambie, Nika Salia
We present equivalent formulations for concepts related to set families for which every subfamily with empty intersection has a bounded sub-collection with empty intersection. Here…
Edges not covered by monochromatic bipartite graphs
Xiutao Zhu, Ervin Győri, Zhen He +4
Let denote the maximum number of edges not contained in any monochromatic copy of~ in a -coloring of the edges of , and let denote the Turán number…
Generalized Turan number for the edge blow-up graph
Zequn Lv, Ervin Győri, Zhen He +4
Let be a graph and be an integer. The edge blow-up of is the graph obtained from replacing each edge in by a copy of where the new vertices of the cliqu…
Exact results for generalized extremal problems forbidding an even cycle
Ervin Győri, Zhen He, Zequn Lv +4
We determine the maximum number of copies of in a -free -vertex graph for all integers and sufficiently large . Moreover, for and…
Stability version of Dirac's theorem and its applications for generalized Turán problems
Xiutao Zhu, Ervin Győri, Zhen He +3
In 1952, Dirac proved that every -connected -vertex graph with the minimum degree contains a cycle of length at least . Here we obtain a stability ve…
The maximum number of copies of an even cycle in a planar graph
Zequn Lv, Ervin Győri, Zhen He +3
We resolve a conjecture of Cox and Martin by determining asymptotically for every the maximum number of copies of in an -vertex planar graph.
Subgraph densities in -free graphs
Andrzej Grzesik, Ervin Győri, Nika Salia +1
In this paper we disprove a conjecture of Lidický and Murphy about the number of copies of a given graph in a -free graph and give an alternative general conjecture. We also p…
Extremal results for graphs avoiding a rainbow subgraph
Peter Frankl, Ervin Győri, Zhen He +5
We say that graphs on a common vertex set of size contain a rainbow copy of a graph if their union contains a copy of with each edge belonging t…
Pósa-type results for Berge-hypergraphs
Nika Salia
A Berge cycle of length in a hypergraph is a sequence of distinct vertices and hyperedges such that for al…