In the 1960's, Erdős and Gallai conjectured that the edges of any n-vertex graph can be
decomposed into O (n) cycles and edges. We improve upon the previous best bound of O (n …

We study polynomial-time approximation algorithms for edge and vertex Sparsest Cut and
Small Set Expansion in terms of k, the number of edges or vertices cut in the optimal …

The vertex expansion of graph is a fundamental graph parameter. Given a graph G=(V, E)
and a parameter δ∈(0, 1/2], its δ-SSVE is defined as where∂ V (S) is the vertex boundary of …

Strong Parallel Repetition for Unique Games on Small Set Expanders The strong parallel
repetition problem for unique games is to efficiently reduce the 1-delta vs. 1-C* delta gap …

Constraint satisfaction problems (CSPs) are ubiquitous in theoretical computer science. We
study the problem of StrongCSPs, ie instances where a large induced sub-instance has a …

The problem of finding the largest induced balanced bipartite subgraph in a given graph is
NP-hard. This problem is closely related to the problem of finding the smallest Odd Cycle …