Bounds on the k-domination number of a graph

Ermelinda DeLaViña, Wayne Goddard, Michael A. Henning, Ryan Pepper, Emil R. Vaughan
<span title="">2011</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="" style="color: black;">Applied Mathematics Letters</a> </i> &nbsp;
The k-domination number of a graph is the cardinality of a smallest set of vertices such that every vertex not in the set is adjacent to at least k vertices of the set. We prove two bounds on the k-domination number of a graph, inspired by two conjectures of the computer program Graffiti.pc. In particular, we show that for any graph with minimum degree at least 2k − 1, the k-domination number is at most the matching number.
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="">doi:10.1016/j.aml.2011.01.013</a> <a target="_blank" rel="external noopener" href="">fatcat:gkudp7yb75gvbim6yuesmvkjge</a> </span>
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