Resumen
Consider a graph G which belongs to a graph class ??
C
. We are interested in connecting a node ?????(??)
w
?
V
(
G
)
to G by a single edge ????
u
w
where ?????(??)
u
?
V
(
G
)
; we call such an edge a tail. As the graph resulting from G after the addition of the tail, denoted ??+????
G
+
u
w
, need not belong to the class ??
C
, we want to compute the number of non-edges of G in a minimum ??
C
-completion of ??+????
G
+
u
w
, i.e., the minimum number of non-edges (excluding the tail ????
u
w
) to be added to ??+????
G
+
u
w
so that the resulting graph belongs to ??
C
. In this paper, we study this problem for the classes of split, quasi-threshold, threshold and ??4
P
4
-sparse graphs and we present linear-time algorithms by exploiting the structure of split graphs and the tree representation of quasi-threshold, threshold and ??4
P
4
-sparse graphs.