A spanning tree of a graph such that each vertex in the tree has degree at most d is called a degree-constrained spanning tree. The problem of finding the degree-constrained spann...
We consider the problem of finding a sparse set of edges containing the minimum spanning tree (MST) of a random subgraph of G with high probability. The two random models that we ...
We introduce the weak gap property for directed graphs whose vertex set S is a metric space of size n. We prove that, if the doubling dimension of S is a constant, any directed gra...
For a graph G = (V, E) we consider vertex-k-labellings f : V → {1, 2, . . . , k} for which the induced edge weighting w : E → {2, 3, . . . , 2k} with w(uv) = f(u) + f(v) is inj...
Stephan Brandt, Jozef Miskuf, Dieter Rautenbach, F...
In a finite simple undirected graph, a vertex is simplicial if its neighborhood is a clique. We say that, for k 2, a graph G = (VG, EG) is the k-simplicial power of a graph H = (V...