Domination and total domination on asteroidal triple-free graphs
نویسندگان
چکیده
منابع مشابه
Domination and Total Domination on Asteroidal Triple-free Graphs
We present the first polynomial time algorithms for solving the NPcomplete graph problems DOMINATING SET and TOTAL DOMINATING SET when restricted to asteroidal triple-free graphs. We also present algorithms to compute a minimum cardinality dominating set and a minimum cardinality total dominating set on a large superclass of the asteroidal triple-free graphs, called DDP-graphs. These algorithms...
متن کاملConnected Domination and Steiner Set on Asteroidal Triple-Free Graphs
An asteroidal triple is a set of three independent vertices such that between any two of them there exists a path that avoids the neighl.)ourhood of the third. Graphs that do not. co~,tain an asteroidal triple are called asteroidal triple-free (AT-free) graphs. AT-free graphs strictly contain the well-known class of cocomparability graphs, and are not necessarily perfect.. We present efficient,...
متن کاملOn graphs with equal total domination and connected domination numbers
A subset S of V is called a total dominating set if every vertex in V is adjacent to some vertex in S. The total domination number γt (G) of G is the minimum cardinality taken over all total dominating sets of G. A dominating set is called a connected dominating set if the induced subgraph 〈S〉 is connected. The connected domination number γc(G) of G is the minimum cardinality taken over all min...
متن کاملAsteroidal Triple-Free Graphs
An independent set of three vertices such that each pair is joined by a path that avoids the neighborhood of the third is called an asteroidal triple. A graph is asteroidal triple-free (AT-free) if it contains no asteroidal triples. The motivation for this investigation was provided, in part, by the fact that the AT-free graphs provide a common generalization of interval, permutation, trapezoid...
متن کاملOn Total Domination in Graphs
LetG = (V,E) be a finite, simple, undirected graph. A set S ⊆ V is called a total dominating set if every vertex of V is adjacent to some vertex of S. Interest in total domination began when the concept was introduced by Cockayne, Dawes, and Hedetniemi [6] in 1980. In 1998, two books on the subject appeared ([11] and [12]), followed by a survey of more recent results in 2009 [15]. The total dom...
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: Discrete Applied Mathematics
سال: 2000
ISSN: 0166-218X
DOI: 10.1016/s0166-218x(99)00128-6