On the number of minimum dominating sets and total dominating sets in forests
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Peer-reviewed
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Abstract
Abstract We show that the maximum number of minimum dominating sets of a forest with domination number is at most and construct for each a tree with domination number that has more than minimum dominating sets. Furthermore, we disprove a conjecture about the number of minimum total dominating sets in forests by Henning, Mohr and Rautenbach.
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Publication status: Published
Funder: Trinity College, University of Cambridge; doi: http://dx.doi.org/10.13039/501100000727
Funder: Department of Pure Mathematics and Mathematical Statistics of the University of Cambridge
Funder: Cambridge Commonwealth, European and International Trust
Journal Title
Journal of Graph Theory
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Journal ISSN
0364-9024
1097-0118
1097-0118
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Publisher
Wiley
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Except where otherwised noted, this item's license is described as http://creativecommons.org/licenses/by/4.0/
Sponsorship
Engineering and Physical Sciences Research Council (EP/V52024X/1, EP/T517847/1)