3 papers
math.CO2023
On triangle-free graphs maximizing embeddings of bipartite graphs
Dmitriy Gorovoy, Andrzej Grzesik, Justyna Jaworska
In 1991 Gy\H ori, Pach, and Simonovits proved that for any bipartite graph containing a matching avoiding at most 1 vertex, the maximum number of copies of in any large eno…
math.CO2023
Directed graphs without rainbow triangles
Sebastian Babiński, Andrzej Grzesik, Magdalena Prorok
One of the most fundamental results in graph theory is Mantel's theorem which determines the maximum number of edges in a triangle-free graph of order . Recently a colorful vari…
math.CO2023
Turán problems for oriented graphs
Andrzej Grzesik, Justyna Jaworska, Bartłomiej Kielak +2
A classical Turán problem asks for the maximum possible number of edges in a graph of a given order that does not contain a particular graph as a subgraph. It is well-known tha…