6 papers · 1 filter
Edge-disjoint cycles with the same vertex set
Debsoumya Chakraborti, Oliver Janzer, Abhishek Methuku +1
In 1975, Erdős asked for the maximum number of edges that an -vertex graph can have if it does not contain two edge-disjoint cycles on the same vertex set. It is known that Turá…
Tight general bounds for the extremal numbers of 0-1 matrices
Barnabás Janzer, Oliver Janzer, Van Magnan +1
A zero-one matrix is said to contain another zero-one matrix if we can delete some rows and columns of and replace some -entries with -entries such that the resul…
On the generalized Turán problem for odd cycles
Csongor Beke, Oliver Janzer
In 1984, Erdős conjectured that the number of pentagons in any triangle-free graph on vertices is at most , which is sharp by the balanced blow-up of a pentagon. This…
On locally rainbow colourings
Barnabás Janzer, Oliver Janzer
Given a graph , let denote the smallest for which the following holds. We can assign a -colouring of the edge set of to each vertex in with…
Regular subgraphs of linear hypergraphs
Oliver Janzer, Benny Sudakov, István Tomon
We prove that the maximum number of edges in a 3-uniform linear hypergraph on vertices containing no 2-regular subhypergraph is . This resolves a conjecture of Dell…
Small subgraphs with large average degree
Oliver Janzer, Benny Sudakov, István Tomon
In this paper we study the fundamental problem of finding small dense subgraphs in a given graph. For a real number , we prove that every graph on vertices with average de…