TY - JOUR
T1 - On disconnected cuts and separators
AU - Ito, Takehiro
AU - Kamiski, Marcin
AU - Paulusma, Danil
AU - Thilikos, Dimitrios M.
N1 - Funding Information:
The third author was supported by EPSRC grant, EP/G043434/1 .
Funding Information:
The fourth author was supported by the project “Kapodistrias” (A Π 02839/28.07.2008) of the National and Kapodistrian University of Athens (project code: 70/4/8757).
PY - 2011/8/6
Y1 - 2011/8/6
N2 - 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 is NP-complete. We also show that the problem of testing whether a graph has a disconnected cut separating two specified vertices, s and t, is NP-complete.
AB - 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 is NP-complete. We also show that the problem of testing whether a graph has a disconnected cut separating two specified vertices, s and t, is NP-complete.
KW - 2-partition
KW - Compaction
KW - Cut set
KW - Retraction
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U2 - 10.1016/j.dam.2011.04.027
DO - 10.1016/j.dam.2011.04.027
M3 - Article
AN - SCOPUS:79959552582
VL - 159
SP - 1345
EP - 1351
JO - Discrete Applied Mathematics
JF - Discrete Applied Mathematics
SN - 0166-218X
IS - 13
ER -