Date: October 25, 2018 16:15–17:00

Place: Exactum C122 (Kumpula)

Speaker: Syed Meesum (Wroclaw)

**Title**: Rank Vertex Cover as a Natural Problem for Algebraic Compression

**Abstract**: The question of the existence of a polynomial kernelization of the Vertex Cover Above LP problem was a longstanding, notorious open problem in Parameterized Complexity. Six years ago, the breakthrough work by Kratsch and Wahlstr ̈om on representative sets finally answered this question in the affirmative [FOCS 2012]. In this talk, I will present an alternative, algebraic compression of the Vertex Cover Above LP problem into the Rank Vertex Cover problem. Here, the input consists of a graph G, a parameter k, and a bijection between V(G) and the set of columns of a representation of a matroid M, and the objective is to find a vertex cover whose rank is upper bounded by k.