Convexity of minimal dominating functions of trees — II
نویسندگان
چکیده
منابع مشابه
Minimal trees and monophonic convexity
Let V be a finite set and M a collection of subsets of V . Then M is an alignment of V if and only if M is closed under taking intersections and contains both V and the empty set. If M is an alignment of V , then the elements of M are called convex sets and the pair (V,M) is called an alignment or a convexity. If S ⊆ V , then the convex hull of S is the smallest convex set that contains S. Supp...
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Domination in graphs’ has been studied extensively and at present it is an emerging area of research in graph theory. An introduction and an extensive overview on domination in graphs and related topics is surveyed and detailed in the two books by Haynes et al. [1,2]. Product of graphs occurs naturally in discrete mathematics as tools in combinatorial constructions. They give rise to an importa...
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‘Domination in graphs’ has been studied extensively and at present it is an emerging area of research in graph theory. An introduction and an extensive overview on domination in graphs and related topics is surveyed and detailed in the two books by Haynes et al. [1,2]. Product of graphs occurs naturally in discrete mathematics as tools in combinatorial constructions. They give rise to an import...
متن کاملTrees having many minimal dominating sets
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.
متن کاملMinimal 2-dominating sets in trees
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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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1994
ISSN: 0012-365X
DOI: 10.1016/0012-365x(94)90154-6