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On Finding the Maximum Number of Disjoint Cuts in Seymour Graphs ?
 

Summary: On Finding the Maximum Number of Disjoint
Cuts in Seymour Graphs ?
Alexander A. Ageev
Sobolev Institute of Mathematics
pr. Koptyuga 4, 630090, Novosibirsk, Russia
ageev@math.nsc.ru
Abstract. In the CUT PACKING problem, given an undirected con­
nected graph G, it is required to find the maximum number of pairwise
edge disjoint cuts in G. It is an open question if CUT PACKING is
NP­hard on general graphs. In this paper we prove that the problem is
polynomially solvable on Seymour graphs which include both all bipar­
tite and all series­parallel graphs. We also consider the weighted version
of the problem in which each edge of the graph G has a nonnegative
weight and the weight of a cut D is equal to the maximum weight of
edges in D. We show that the weighted version is NP­hard even on cubic
planar graphs.
1 Introduction
In the CUT PACKING problem, given an undirected connected graph G, it
is required to find the maximum number of pairwise edge disjoint cuts in G.
This problem looks natural and has various connections with many well­known

  

Source: Ageev, Alexandr - Sobolev Institute of Mathematics, Russian Academy of Sciences, Novosibirsk

 

Collections: Mathematics