The bondage number of random graphs
Abstract
A dominating set of a graph is a subset
D
of its vertices such that every vertex not in
D
is adjacent to at least one member of
D
. The domination number of a graph
G
is the number of vertices in a smallest dominating set of
G
. The bondage number of a nonempty graph
G
is the size of a smallest set of edges whose removal from
G
results in a graph with domination number greater than the domination number of
G
. In this note, we study the bondage number of binomial random graph
G(n,p)
. We obtain a lower bound that matches the order of the trivial upper bound. As a side product, we give a one-point concentration result for the domination number of
G(n,p)
under certain restrictions.