3 citations · 5 across the 3 of their papers we have counts for
5 papers · 1 filter
Note on the second eigenvalue of regular graphs
Igor Balla, Eero Räty, Benny Sudakov +1
The goal of this expository note is to give a short, self-contained proof of nearly optimal lower bounds for the second largest eigenvalue of the adjacency matrix of regular graphs…
Orthonormal representations of -free graphs
Igor Balla, Shoham Letzter, Benny Sudakov
Let be unit vectors such that among any three there is an orthogonal pair. How large can be as a function of , and how large can the leng…
The Minrank of Random Graphs over Arbitrary Fields
Noga Alon, Igor Balla, Lior Gishboliner +2
The minrank of a graph on the set of vertices over a field is the minimum possible rank of a matrix with nonzero diagonal entrie…
A remark on Hamilton cycles with few colors
Igor Balla, Alexey Pokrovskiy, Benny Sudakov
Akbari, Etesami, Mahini, and Mahmoody conjectured that every proper edge colouring of with colours contains a Hamilton cycle with colours. They proved th…
Minimum density of union-closed families
Igor Balla
Let F be a finite union-closed family of sets whose largest set contains n elements. In \cite{Wojcik92}, Wojcik defined the density of F to be the ratio of the average set size of…