Decompositions of multigraphs into parts with two edges
Jaroslav Ivančo, Mariusz Meszka, Zdzisław Skupień (2002)
Discussiones Mathematicae Graph Theory
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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.