Geodesic
Domination Number of Graphs with Minimum Degree Five
Discussiones Mathematicae. Graph Theory, Tome 41 (2021) no. 3, pp. 763-777

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We prove that for every graph G on n vertices and with minimum degree five, the domination number γ(G) cannot exceed n/3. The proof combines an algorithmic approach and the discharging method. Using the same technique, we provide a shorter proof for the known upper bound 4n/11 on the domination number of graphs of minimum degree four.
Keywords: dominating set, domination number, discharging method 
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     title = {Domination {Number} of {Graphs} with {Minimum} {Degree} {Five}},
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Bujtás, Csilla. Domination Number of Graphs with Minimum Degree Five. Discussiones Mathematicae. Graph Theory, Tome 41 (2021) no. 3, pp. 763-777. http://geodesic.mathdoc.fr/item/DMGT_2021_41_3_a4/