  Chemical reactions can be understood as transformations of multigraphs
(molecules) that preserve vertex labels (atoms) and degrees (sums of bonding
and non-bonding electrons), thereby implying the atom-atom map of a reaction.
The corresponding reaction mechanism is often described by an electron pushing
diagram that explains the transformation by consecutive local relocations of
invidudal edges (electron pairs). Here, we show that every degree-preserving
map between multigraphs, and thus every atom-atom map, can be generated by
cyclic electron pushing. Moreover, it is always possible to decompose such an
explanation into electron pushing diagrams involving only four electron pairs.
This in turn implies that every reaction can be decomposed into a sequence of
elementary reactions that involve at most two educt molecules and two product
molecules. Hence, the requirement of a mechanistic explantion in terms of
electron pushing and small imaginary transition states does not impose a
combinatorial constraint on the feasibility of hypothetical chemical reactions.
