In Section 3, we introduced the graph induced by two
trees 
and 
as the complete bipartite graph 
, with 
and 
(where 
and 
are the nodes of and
, respectively). Let 
be an edit script that transforms
to ; that is, 
.
We now define the edge cover 
induced by .
Intuitively, we obtain as follows. Create a copy 
of
, and introduce an edge between each node in and its copy
in . Apply the edit script to , moving, copying, etc. the
end-points of the edges with the nodes they are attached to as nodes
are moved, copied, etc. Thus, when an a node 
is copied,
producing node n', any edge [m, n] is split to produce an new edge
[m, n']. The other edit operations are handled analogously.
Furthermore, an edge between the special nodes 
and 
is added initially, and removed when it is no longer needed
to cover either or . Due to space
limitations, we illustrate the definition of the edge cover induced by
an edit script informally using an example; the formal definition is
in [&make_named_href('',
"node21.html#bbdiffExtended","[CGM97]")].
Figure: Example 4.1: the initial edge cover
