<s>
An	O
ordered	B-Application
graph	I-Application
is	O
a	O
graph	O
with	O
a	O
total	O
order	O
over	O
its	O
nodes	O
.	O
</s>
<s>
In	O
an	O
ordered	B-Application
graph	I-Application
,	O
the	O
parents	O
of	O
a	O
node	O
are	O
the	O
nodes	O
that	O
are	O
adjacent	O
to	O
it	O
and	O
precede	O
it	O
in	O
the	O
ordering	O
.	O
</s>
<s>
More	O
precisely	O
,	O
is	O
a	O
parent	O
of	O
in	O
the	O
ordered	B-Application
graph	I-Application
if	O
and	O
.	O
</s>
<s>
The	O
width	O
of	O
a	O
node	O
is	O
the	O
number	O
of	O
its	O
parents	O
,	O
and	O
the	O
width	O
of	O
an	O
ordered	B-Application
graph	I-Application
is	O
the	O
maximal	O
width	O
of	O
its	O
nodes	O
.	O
</s>
<s>
The	O
induced	O
graph	O
of	O
an	O
ordered	B-Application
graph	I-Application
is	O
obtained	O
by	O
adding	O
some	O
edges	O
to	O
an	O
ordering	O
graph	O
,	O
using	O
the	O
method	O
outlined	O
below	O
.	O
</s>
<s>
The	O
induced	O
width	O
of	O
an	O
ordered	B-Application
graph	I-Application
is	O
the	O
width	O
of	O
its	O
induced	O
graph	O
.	O
</s>
<s>
Given	O
an	O
ordered	B-Application
graph	I-Application
,	O
its	O
induced	O
graph	O
is	O
another	O
ordered	B-Application
graph	I-Application
obtained	O
by	O
joining	O
some	O
pairs	O
of	O
nodes	O
that	O
are	O
both	O
parents	O
of	O
another	O
node	O
.	O
</s>
<s>
As	O
an	O
example	O
,	O
the	O
induced	O
graph	O
of	O
an	O
ordered	B-Application
graph	I-Application
is	O
calculated	O
.	O
</s>
