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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.
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Submitted on : Tuesday, March 22, 2016 - 12:56:30 PM
Last modification on : Thursday, August 4, 2022 - 4:54:24 PM
Long-term archiving on: : Sunday, November 13, 2016 - 10:39:19 PM


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  • HAL Id : hal-01291961, version 1



Dieter Mitsche, Xavier Pérez-Giménez, Pawel Pralat. The bondage number of random graphs. The Electronic Journal of Combinatorics, Open Journal Systems, 2016. ⟨hal-01291961⟩



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