A directed multigraph is said to be d-regular if the indegree and outdegree of every vertex is exactly d. By Hall’s theorem one can represent such a multigraph as a combination ...
We present a distributed algorithm that finds a maximal edge packing in O(∆ + log∗ W) synchronous communication rounds in a weighted graph, independent of the number of nodes...
The problem of efficiently monitoring the network flow is regarded as the one to find out the minimum weighted weak vertex cover set for a given graph G = (V, E) with weight func...
Given a directed graph G with non negative cost on the arcs, a directed tree cover of G is a directed tree such that either head or tail (or both of them) of every arc in G is touc...
We consider a special subgraph of a weighted directed graph: one comprising only the k heaviest edges incoming to each vertex. We show that the maximum weight branching in this su...