Algorithmic Aspects of Upper Domination
نویسندگان
چکیده
In this paper we study combinatorial and algorithmic resp. complexity questions of upper domination, i.e., the maximum cardinality of a minimal dominating set in a graph. We give a full classification of the related maximisation and minimisation problems, as well as the related parameterised problems, on general graphs and on graphs of bounded degree, and we also study planar graphs.
منابع مشابه
Algorithmic Aspects of Upper Domination: A Parameterised Perspective
This paper studies Upper Domination, i.e., the problem of computing the maximum cardinality of a minimal dominating set in a graph, with a focus on parameterised complexity. Our main results include W[1]-hardness for Upper Domination, contrasting FPT membership for the parameterised dual Co-Upper Domination. The study of structural properties also yields some insight into Upper Total Domination...
متن کاملThe algorithmic complexity of signed domination in graphs
A two-valued function f defined on the vertices of a graph G (V, E), I : V -+ {-I, I}, is a signed dominating function if the sum of its function values over any closed neighborhood is at least one. That is, for every v E V, f(N[v]) 2: 1, where N(v] consists of v and every vertex adjacent to v. The of a signed dominating function is ICV) = L f( v), over all vertices v E V. The signed domination...
متن کاملOn trees attaining an upper bound on the total domination number
A total dominating set of a graph $G$ is a set $D$ of vertices of $G$ such that every vertex of $G$ has a neighbor in $D$. The total domination number of a graph $G$, denoted by $gamma_t(G)$, is~the minimum cardinality of a total dominating set of $G$. Chellali and Haynes [Total and paired-domination numbers of a tree, AKCE International ournal of Graphs and Combinatorics 1 (2004), 6...
متن کاملSome Algorithmic Results on Restrained Domination in Graphs
A set D ⊆ V of a graph G = (V,E) is called a restrained dominating set of G if every vertex not in D is adjacent to a vertex in D and to a vertex in V \D. The MINIMUM RESTRAINED DOMINATION problem is to find a restrained dominating set of minimum cardinality. Given a graph G, and a positive integer k, the RESTRAINED DOMINATION DECISION problem is to decide whether G has a restrained dominating ...
متن کاملImproved Upper Bounds on the Domination Number of Graphs With Minimum Degree at Least Five
An algorithmic upper bound on the domination number γ of graphs in terms of the order n and the minimum degree δ is proved. It is demonstrated that the bound improves best previous bounds for any 5 ≤ δ ≤ 50. In particular, for δ = 5, Xing et al. proved in 2006 that γ ≤ 5n/14 < 0.3572n. This bound is improved to 0.3440n. For δ = 6, Clark et al. in 1998 established γ < 0.3377n, while Biró et al. ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- CoRR
دوره abs/1506.07260 شماره
صفحات -
تاریخ انتشار 2015