For
a nonempty finite
vertex set A in
a degree-
k regular tree, its induced
forest has
∣A∣−c(A) edges, where
c(A) counts its components. Summing degrees and subtracting twice the internal
edge count gives the displayed
number of
edges with exactly one endpoint in
A. In particular it is at least
(k−2)∣A∣+2.
