2005 European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05)
Stefan Felsner (ed.)
DMTCS Conference Volume AE (2005), pp. 231234
author:  Miri Priesler and Michael Tarsi 

title:  Multigraph decomposition into multigraphs with two underlying edges 
keywords:  Decomposition, Multigraph, NPC 
abstract: 
Due to some intractability considerations, reasonable
formulation of necessary and sufficient conditions for
decomposability of a general multigraph
G
into a fixed connected multigraph
H
, is probably not feasible if the underlying simple
graph of
H
has three or more edges. We study the case where
H
consists of two underlying edges. We present
necessary and sufficient conditions for
H
decomposability of
G
, which hold when certain size parameters of
G
lies within some bounds which depends on the
multiplicities of the two edges of
H
. We also show this result to be "tight" in the sense
that even a slight deviation of these size parameters from
the given bounds results intractability of the
corresponding decision problem.

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reference:  Miri Priesler and Michael Tarsi (2005), Multigraph decomposition into multigraphs with two underlying edges, in 2005 European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05), Stefan Felsner (ed.), Discrete Mathematics and Theoretical Computer Science Proceedings AE, pp. 231234 
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