The routing number rt(G) of a connected graph G is the minimum integer r so that every permutation of vertices can be routed in r steps by swapping the ends of disjoint edges. In t...
Given a k-uniform hypergraph on n vertices, partitioned in k equal parts such that every hyperedge includes one vertex from each part, the k-Dimensional Matching problem asks wheth...
We consider a dense n-user Gaussian interference network formed by paired transmitters and receivers placed independently at random in Euclidean space. Under natural conditions on ...
Matthew Aldridge, Oliver Johnson, Robert J. Piecho...
: We study a random graph model which is a superposition of bond percolation on Zd with parameter p, and a classical random graph G(n, c/n). We show that this model, being a homoge...
Coloring a k-colorable graph using k colors (k ≥ 3) is a notoriously hard problem. Considering average case analysis allows for better results. In this work we consider the unif...
Amin Coja-Oghlan, Michael Krivelevich, Dan Vilench...