|کد مقاله||کد نشریه||سال انتشار||مقاله انگلیسی||ترجمه فارسی||نسخه تمام متن|
|4949891||1364262||2017||9 صفحه PDF||سفارش دهید||دانلود کنید|
We show that interval graphs on n vertices have at most 3n/3â1.4422n minimal dominating sets, and that these can be enumerated in time Oâ(3n/3). As there are examples of interval graphs that actually have 3n/3 minimal dominating sets, our bound is tight. We show that the same upper bound holds also for trees, i.e.Â trees on n vertices have at most 3n/3â1.4422n minimal dominating sets. The previous best upper bound on the number of minimal dominating sets in trees was 1.4656n, and there are trees that have 1.4167n minimal dominating sets. Hence our result narrows this gap. On general graphs there is a larger gap, with 1.7159n being the best known upper bound, whereas no graph with 1.5705n or more minimal dominating sets is known.
Journal: Discrete Applied Mathematics - Volume 216, Part 1, 10 January 2017, Pages 162-170