NP-completeness results for partitioning a graph into total dominating sets
نویسندگان
چکیده
منابع مشابه
Partitioning a Graph into a Dominating Set, a Total Dominating Set, and something else 1Michael
A recent result of Henning and Southey (A note on graphs with disjoint dominating and total dominating set, Ars Comb. 89 (2008), 159–162) implies that every connected graph of minimum degree at least three has a dominating set D and a total dominating set T which are disjoint. We show that the Petersen graph is the only such graph for which D ∪ T necessarily contains all vertices of the graph.
متن کاملPartitioning Graphs into Generalized Dominating Sets
We study the computational complexity of partitioning the vertices of a graph into generalized dominating sets. Generalized dominating sets are parameterized by two sets of nonnegative integers and which constrain the neighborhood N (v) of vertices. A set S of vertices of a graph is said to be a (;)-set if 8v 2 S : jN(v) \ Sj 2 and 8v 6 2 S : jN(v) \ Sj 2 .
متن کاملPartitioning a graph into convex sets
Let G be a finite simple graph. Let S ⊆ V (G), its closed interval I[S] is the set of all vertices lying on a shortest path between any pair of vertices of S. The set S is convex if I[S] = S. In this work we define the concept of convex partition of graphs. If there exists a partition of V (G) into p convex sets we say that G is p-convex. We prove that is NP -complete to decide whether a graph ...
متن کاملPartitioning a graph into alliance free sets
A strong defensive alliance in a graph G = (V, E) is a set of vertices A ⊆ V , for which every vertex v ∈ A has at least as many neighbors in A as in V − A. We call a partition A, B of vertices to be an alliance-free partition, if neither A nor B contains a strong defensive alliance as a subset. We prove that a connected graph G has an alliance-free partition exactly when G has a block that is ...
متن کاملNP - completeness Results for NONOGRAM
We introduce a new class of NP problems called ANOTHER SOLUTION PROBLEMs. For a given NP problem X, ANOTHER SOLUTION PROBLEM for X (ASP for X) is to ask, for a given instance I for X and its solution, whether there is another solution for I. The di culty of ASP for X may not be immediate from the di culty of X. For example, for some NP-complete problems such as 3SAT or 3DM, it is easy to show t...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Theoretical Computer Science
سال: 2020
ISSN: 0304-3975
DOI: 10.1016/j.tcs.2018.04.006