Flipping in Acyclic and Strongly Connected Graphs
نویسنده
چکیده
A flippable edge in an acyclic digraph is an edge whose reorientation leaves the graph acyclic. We characterize the spanning trees T of an undirected graph G such that there exists an acyclic orientation of G whose set of flippable edges is T . In particular for every edge e ∈ E(G) we give a linear algorithm returning an acyclic orientation and a spanning tree T containing e such that T is the set of flippable edges of the digraph. After going to oriented matroid theory and dualizing the proofs we obtain similar results for flippable edges in strongly connected digraphs.
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