https://hal.inria.fr/hal-01291961Mitsche, DieterDieterMitscheUNS - Université Nice Sophia Antipolis (1965 - 2019) - COMUE UCA - COMUE Université Côte d'Azur (2015-2019)Pérez-Giménez, XavierXavierPérez-GiménezRyerson University [Toronto]Pralat, PawelPawelPralatRyerson University [Toronto]The bondage number of random graphsHAL CCSD2016[MATH.MATH-PR] Mathematics [math]/Probability [math.PR][MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO]Mitsche, Dieter2016-03-22 12:56:302022-08-04 16:54:242016-09-06 12:10:38enJournal articlesapplication/pdf1A 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.