Detecting Tampering in a Random Hypercube · arXivDeskAbstract
Consider the random hypercube H2n(pn) obtained from the hypercube H2n
by deleting any given edge with probabilty
, independently of all the other edges. A diameter path in
is a longest geodesic path in
. Consider the following two ways of tampering with the random graph
H2n(pn) : (i) choose a diameter path at random and adjoin all of its edges to
H2n(pn) ; (ii) choose a diameter path at random from among those that start at
0=(0,...,0) , and adjoin all of its edges to
H2n(pn) . We study the question of whether these tamperings are detectable asymptotically as
.