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1 vote
2 answers
107 views

Minimum edge-weighted directed subgraph in polynomial time

I am looking for an algorithm with polynomial complexity where, given a strongly connected edge-weighted digraph I can find the minimal subgraph which connects some root vertex v to a known set of ...
2 votes
1 answer
156 views

Directed version of this lemma

On a paper by Shoham Letzter, available Here, there's a lemma that says as follows: Lemma 0: For every graph $G$, there exist two disjoint sets $U,W\subseteq V(G)$ of equal size, such that there are ...
6 votes
0 answers
69 views

Digraph weak connectivity in $O(V)$ space and $O(V+E)$ time

A digraph is called weakly connected if its underlying undirected graph is connected. You are given a digraph $G$ with $V$ vertices and $E$ edges as a read-only data structure consisting of lists of ...