We present the first local approximation schemes for maximum independent set and minimum vertex cover in unit disk graphs. In the graph model we assume that each node knows its geo...
In [13], Erd˝os et al. defined the local chromatic number of a graph as the minimum number of colors that must appear within distance 1 of a vertex. For any ∆ ≥ 2, there are ...
Consider a tree T and a forest F. The paper discusses the following new problems: The Forest vertex-cover problem (FVC): cover the vertices of T by a minimum number of copies of tr...
Computing a minimum vertex cover in graphs and hypergraphs is a well-studied optimizaton problem. While intractable in general, it is well known that on bipartite graphs, vertex c...
Let A be the edge-node incidence matrix of a bipartite graph G = (U, V ; E), I be a subset the nodes of G, and b be a vector such that 2b is integral. We consider the following mi...