Given a family 𝓕 of multigraphs without isolated vertices, a multigraph M is called 𝓕-decomposable if M is an edge disjoint union of multigraphs each of which is isomorphic to a member of 𝓕. We present necessary and sufficient conditions for the existence of such decompositions if 𝓕 comprises two multigraphs from the set consisting of a 2-cycle, a 2-matching and a path with two edges.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1162, author = {Jaroslav Ivan\v co and Mariusz Meszka and Zdzis\l aw Skupie\'n}, title = {Decompositions of multigraphs into parts with two edges}, journal = {Discussiones Mathematicae Graph Theory}, volume = {22}, year = {2002}, pages = {113-121}, zbl = {1018.05086}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1162} }
Jaroslav Ivančo; Mariusz Meszka; Zdzisław Skupień. Decompositions of multigraphs into parts with two edges. Discussiones Mathematicae Graph Theory, Tome 22 (2002) pp. 113-121. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1162/
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