We study the inapproximability of Vertex Cover and Independent Set on degree d graphs. We prove that: • Vertex Cover is Unique Games-hard to approximate to within a factor 2−(...
An equivalence graph is a disjoint union of cliques, and the equivalence number eq(G) of a graph G is the minimum number of equivalence subgraphs needed to cover the edges of G. W...
We present the first local approximation schemes for maximum independent set and minimum vertex cover in unit disk graphs. In the graph model we assume that each node knows its geo...
Abstract. Possibly the most famous algorithmic meta-theorem is Courcelle's theorem, which states that all MSO-expressible graph properties are decidable in linear time for gra...
It has been a challenging open problem whether there is a polynomial time approximation algorithm for the Vertex Cover problem whose approximation ratio is bounded by a constant l...