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 -