Geodesic
Multigraph decomposition into multigraphs with two underlying edges
Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AE, European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05), DMTCS Proceedings vol. AE, European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05) (2005).

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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. 
@article{DMTCS_2005_special_250_a14,
     author = {Priesler, Miri and Tarsi, Michael},
     title = {Multigraph decomposition into multigraphs with two underlying edges},
     journal = {Discrete mathematics & theoretical computer science},
     publisher = {mathdoc},
     volume = {DMTCS Proceedings vol. AE, European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05)},
     year = {2005},
     doi = {10.46298/dmtcs.3405},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.3405/}
}
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%V DMTCS Proceedings vol. AE, European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05)
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Priesler, Miri; Tarsi, Michael. Multigraph decomposition into multigraphs with two underlying edges. Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AE, European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05), DMTCS Proceedings vol. AE, European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05) (2005). doi : 10.46298/dmtcs.3405. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.3405/

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