A random geometric graph G(n, r) is a graph resulting from placing n points uniformly at random on the unit area disk, and connecting two points iff their Euclidean distance is at ...
We provide polynomial time data reduction rules for Connected Dominating Set in planar graphs and analyze these to obtain a linear kernel for the planar Connected Dominating Set pr...
While it is exponentially unlikely that a sparse random graph or hypergraph is connected, with probability 1 − o(1) such a graph has a “giant component” that, given its numbe...
In this paper, we study the problem of minimum connected dominating set in geometric k-disk graphs. This research is motivated by the problem of virtual backbone construction in w...
Kai Xing, Wei Cheng, E. K. Park, Shmuel Rotenstrei...
We study the k-wise independent relaxation of the usual model G(N, p) of random graphs where, as in this model, N labeled vertices are fixed and each edge is drawn with probabili...