“…As
by the assumption on
, one can expect that the
th neighbourhood of each vertex
contains almost all vertices in both
and
. A minor modification of [
13, Corollary 2.5] gives precisely this. Namely, it shows that there exists a vertex
such that, for all but
vertices
, there exists a path from
to
(in
) with one vertex in each of
and similarly for
…”