 
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
