Please use this identifier to cite or link to this item: http://repositorio.unicamp.br/jspui/handle/REPOSIP/356196
Type: Pré-print
Title: Computing the largest bond and the maximum connected cut of a graph
Author: Duarte, Gabriel L.
Eto, Hiroshi
Hanaka, Tesshu
Kobayashi, Yasuaki
Kobayashi, Yusuke
Lokshtanov, Daniel
Pedrosa, Lehilton L. C.
Schouery, Rafael C. S.
Souza, Uéverton S.
Abstract: The cut-set ∂(S) of a graph G=(V,E) is the set of edges that have one endpoint in S⊂V and the other endpoint in V∖S, and whenever G[S] is connected, the cut [S,V∖S] of G is called a connected cut. A bond of a graph G is an inclusion-wise minimal disconnecting set of G, i.e., bonds are cut-sets that determine cuts [S,V∖S] of G such that G[S] and G[V∖S] are both connected. Contrasting with a large number of studies related to maximum cuts, there exist very few results regarding the largest bond of general graphs. In this paper, we aim to reduce this gap on the complexity of computing the largest bond, and the maximum connected cut of a graph. Although cuts and bonds are similar, we remark that computing the largest bond and the maximum connected cut of a graph tends to be harder than computing its maximum cut. We show that it does not exist a constant-factor approximation algorithm to compute the largest bond, unless P = NP . Also, we show that LARGEST BOND and MAXIMUM CONNECTED CUT are NP-hard even for planar bipartite graphs, whereas MAXIMUM CUT is trivial on bipartite graphs and polynomial-time solvable on planar graphs. In addition, we show that LARGEST BOND and MAXIMUM CONNECTED CUT are NP-hard on split graphs, and restricted to graphs of clique-width w they can not be solved in time f(w)no(w) unless the Exponential Time Hypothesis fails, but they can be solved in time f(w)nO(w). Finally, we show that both problems are fixed-parameter tractable when parameterized by the size of the solution, the treewidth, and the twin-cover number
Subject: Algoritmos
Country: Estados Unidos
Editor: Springer
Rights: Fechado
Identifier DOI: 10.1007/s00453-020-00789-1
Address: https://link.springer.com/article/10.1007%2Fs00453-020-00789-1
Date Issue: 2021
Appears in Collections:IC - Artigos e Outros Documentos

Files in This Item:
There are no files associated with this item.


Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.