In [13], Erd˝os et al. defined the local chromatic number of a graph as the minimum number of colors that must appear within distance 1 of a vertex. For any ∆ ≥ 2, there are ...
We consider the variant of the minimum vertex cover problem in which we require that the cover induces a connected subgraph. We give new approximation results for this problem in d...
In set-system auctions, there are several overlapping teams of agents, and a task that can be completed by any of these teams. The auctioneer's goal is to hire a team and pay...
Edith Elkind, Leslie Ann Goldberg, Paul W. Goldber...
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...