6 papers
From small eigenvalues to large cuts, and Chowla's cosine problem
Zhihan Jin, Aleksa Milojević, István Tomon +1
We prove that every graph with average degree and smallest adjacency eigenvalue contains a clique of size . A simple corollary of this yields the fi…
Cyclic subsets of tournaments
Zach Hunter, Teng Liu, Aleksa Milojević +1
Let be a Dirac graph, and let be a vertex subset of , chosen uniformly at random. How likely is the induced subgraph to be Hamiltonian? This question, proposed by…
Beyond the MaxCut problem in -free graphs
Zhihan Jin, Aleksa Milojević, István Tomon
In a recent breakthrough, Zhang proves that if is an -free graph with edges, then has a cut of size at least , making a significant step towards a…
-free subgraphs of high degree with geometric applications
Zach Hunter, Aleksa Milojević, Istvan Tomon +1
The Zarankiewicz problem, a cornerstone problem in extremal graph theory, asks for the maximum number of edges in an -vertex graph that does not contain the complete bipartite g…
Disjoint pairs in set systems and combinatorics of low rank matrices
Zach Hunter, Aleksa Milojević, Benny Sudakov +1
We study and solve several problems in two closely related settings: set families in with many disjoint pairs of sets and low rank matrices with many zero entries. - More…
Long induced paths in -free graphs
Zach Hunter, Aleksa Milojević, Benny Sudakov +1
More than 40 years ago, Galvin, Rival and Sands showed that every -free graph containing an -vertex path must contain an induced path of length , where $f(n)\to…