Characterizing minimal point set dominating sets
نویسندگان
چکیده
منابع مشابه
Minimal Dominating Set Enumeration
Let G be a graph on n vertices and m edges. An edge is written xy (equivalently yx). A dominating set in G is a set of vertices D such that every vertex of G is either in D or is adjacent to some vertex of D. It is said to be minimal if it does not contain any other dominating set as a proper subset. For every vertex x let N [x] be {x} ∪ {y | xy ∈ E}, and for every S ⊆ V let N [S] := ⋃ x∈S N [x...
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We disprove a conjecture by Skupień that every tree of order n has at most 2 minimal dominating sets. We construct a family of trees of both parities of the order for which the number of minimal dominating sets exceeds 1.4167. We also provide an algorithm for listing all minimal dominating sets of a tree in time O(1.4656). This implies that every tree has at most 1.4656 minimal dominating sets.
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We provide an algorithm for listing all minimal 2-dominating sets of a tree of order n in time O(1.3248n). This implies that every tree has at most 1.3248n minimal 2-dominating sets. We also show that this bound is tight.
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In this paper, we are interested in the enumeration of minimal dominating sets in graphs. A polynomial delay algorithm with polynomial space in split graphs is presented. We then introduce a notion of maximal extension (a set of edges added to the graph) that keeps invariant the set of minimal dominating sets, and show that graphs with extensions as split graphs are exactly the ones having chor...
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ژورنال
عنوان ژورنال: AKCE International Journal of Graphs and Combinatorics
سال: 2016
ISSN: 0972-8600,2543-3474
DOI: 10.1016/j.akcej.2016.07.003