A note on non-dominating set partitions in graphs
نویسندگان
چکیده
منابع مشابه
Dominating Set on Bipartite Graphs
Finding a dominating set of minimum cardinality is an NP-hard graph problem, even when the graph is bipartite. In this paper we are interested in solving the problem on graphs having a large independent set. Given a graph G with an independent set of size z, we show that the problem can be solved in time O∗(2n−z), where n is the number of vertices of G. As a consequence, our algorithm is able t...
متن کاملA Note on Non-dominating Ultrafilters
We show that if cov(M) = κ, where κ is a regular cardinal such that ∀λ < κ(2 ≤ κ), then for every unbounded directed family H of size κ there is an ultrafilter UH such that the relativized Mathias forcing M(UH) preserves the unboundedness of H. This improves a result of M. Canjar (see [4, Theorem 10]). We discuss two instances of generic ultrafilters for which the relativized Mathias forcing pr...
متن کاملA note on dominating cycles in 2-connected graphs
Let G be a 2-connected graph on n vertices such that d(x)+ d(y)+ d(z)>/n for all triples of independent vertices x,y,z. We prove that every longest cycle in G is a dominating cycle unless G is a spanning subgraph of a graph belonging to one of four easily specified classes of graphs.
متن کاملCapacitated Dominating Set on Planar Graphs
Capacitated Domination generalizes the classic Dominating Set problem by specifying for each vertex a required demand and an available capacity for covering demand in its closed neighborhood. The objective is to find a minimum-sized set of vertices that can cover all of the graph’s demand without exceeding any of the capacities. In this paper we look specifically at domination with hard-capacit...
متن کاملA Note on Disjoint Dominating Sets in Graphs
The disjoint domination number γγ(G) of a graph G is the minimum cardinality of the union of two disjoint dominating sets in G. The disjoint independent domination number of a graph G is the minimum cardinality of the union of two disjoint independent dominating sets in G. In this paper we study these two parameters. We determine the value of γγ(G) for several graphs and give partial answers to...
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: Discussiones Mathematicae Graph Theory
سال: 2016
ISSN: 1234-3099,2083-5892
DOI: 10.7151/dmgt.1895