Let G = (V, E) be a graph with vertex set V and edge set E. The k-coloring problem is to assign a color (a number chosen in {1, . . . , k}) to each vertex of G so that no edge has...
We consider the following vertex coloring problem. We are given an undirected graph G = (V, E), where each vertex v is associated with a penalty rejection cost rv. We need to choos...
We prove that coloring a 3-uniform 2-colorable hypergraph with c colors is NP-hard for any constant c. The best known algorithm [20] colors such a graph using O(n1/5 ) colors. Our...
Suppose we are given a sequence of n points in the Euclidean plane, and our objective is to construct, on-line, a connected graph that connects all of them, trying to minimize the...
Let (S, d) be a finite metric space, where each element p ∈ S has a non-negative weight w(p). We study spanners for the set S with respect to weighted distance function dw, wher...
Mohammad Ali Abam, Mark de Berg, Mohammad Farshi, ...