We consider the following maximum disjoint paths problem (mdpp). We are given a large network, and pairs of nodes that wish to communicate over paths through the network — the g...
The (undirected) Node Connectivity Augmentation (NCA) problem is: given a graph J = (V, EJ ) and connectivity requirements {r(u, v) : u, v ∈ V }, find a minimum size set I of n...
The dominatingset problemin graphs asks for a minimumsize subset of vertices with the followingproperty: each vertex is required to either be in the dominating set, or adjacent to...
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...
We introduce a new graph parameter, called the Grothendieck constant of a graph G = (V, E), which is defined as the least constant K such that for every A : E R, sup f:V S|V |-1 ...
Noga Alon, Konstantin Makarychev, Yury Makarychev,...