Local linear set on graphs with bounded twin cover number

Abstract

Inspired by recent results for the so-called fair and local linear problems, we define two problems, Local Linear Set and Local Linear Vertex Cover. Here the task is to find a set of vertices X⊆V (which is a vertex cover) of the input graph (V,E) such that the local linear constraints ℓ(v)≤|X∩N(v)|≤u(v) hold for all v∈V; here, ℓ(v) and u(v) are on the input. We prove that both problems are in FPT for the parameter twin cover number (using integer linear programming).