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1
vote
Accepted
Valid orderings for topological sort
A source is a vertex with in-degree zero.
An order of the vertices is a topological order if deleting the vertices in that order deletes only sources.
Hence, you can verify that an order is topologica …
2
votes
Accepted
Checking if there exists a 'source' vertex
Hint: if you find all the strongly connected components in the graph, the quotient graph of the SCCs is a DAG. In this DAG, if there is a meta-node that can reach all the other meta-nodes, you have y …
3
votes
How to edge-color a directed acyclic graph so that every path visits none or all edges of ea...
It sounds to me like the greedy algorithm should work, I'm not able to come up with any counter-examples, however, I haven't had time to try to prove the claim either.
Terminology
Definition. Let $s …