Abstract
For some alpha with 0 < alpha <= 1, a subset X of vertices in a graph G of ordernis an alpha-partial dominating set of G if the set X dominates at least alpha x n vertices in G. The alpha-partial domination number pd(alpha)(G) of G is the minimum cardinality of an alpha-partial dominating set of G. In this paper partial domination of graphs with minimum degree at least 3 is studied. It is proved that if G is a graph of order n and with delta(G) >= 3, then pd(7/8)(G) <= 1/3n. If in addition n >= 60, then pd(9/10) (G) <= 1/3n, and if G is a connected cubic graph of order n >= 28, then pd(13/14) (G) <= 1/3n. Along the way it is shown that there are exactly four connected cubic graphs of order 14 with domination number 5. (c) 2023 The Author(s). Published by Elsevier B.V.