Minimal disconnected cuts in planar graphs
نویسندگان
چکیده
منابع مشابه
Minimal Disconnected Cuts in Planar Graphs
The problem of finding a disconnected cut in a graph is NP-hard in general but polynomial-time solvable on planar graphs. The problem of finding a minimal disconnected cut is also NP-hard but its computational complexity was not known for planar graphs. We show that it is polynomial-time solvable on 3-connected planar graphs but NP-hard for 2-connected planar graphs. Our technique for the first...
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We prove the following theorem. Let G = (V, E) be a planar bipartite graph, embedded in the etrclidean plane. Let 0 and I be two of its faces. Then there exist pairwise edge-disjoint cuts C,, . . . . C, so that for each two vertices u, w with U, w E 0 or V, WE I, the distance from u to w in G is equal to the number of cuts C, separating u and w. This theorem is dual to a theorem of Okamura on p...
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For a connected graph G = (V,E), a subset U ⊆ V is called a disconnected cut if U disconnects the graph and the subgraph induced by U is disconnected as well. A natural condition is to impose that for any u ∈ U the subgraph induced by (V \U)∪{u} is connected. In that case U is called a minimal disconnected cut. We show that the problem of testing whether a graph has a minimal disconnected cut i...
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ژورنال
عنوان ژورنال: Networks
سال: 2016
ISSN: 0028-3045
DOI: 10.1002/net.21696