On dominating sets of maximal outerplanar and planar graphs
نویسندگان
چکیده
منابع مشابه
On dominating sets of maximal outerplanar graphs
A dominating set of a graph is a set S of vertices such that every vertex in the graph is either in S or is adjacent to a vertex in S. The domination number of a graph G, denoted γ (G), is theminimum cardinality of a dominating set ofG. We show that ifG is an n-vertexmaximal outerplanar graph, then γ (G) ≤ (n + t)/4, where t is the number of vertices of degree 2 in G. We show that this bound is...
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Motivated by an application to unstructured multigrid calculations, we consider the problem of asymptotically minimizing the size of dominating sets in triangulated planar graphs. Speci cally, we wish to nd the smallest such that, for n su ciently large, every n-vertex planar graph contains a dominating set of size at most n. We prove that 1 4 13 , and we conjecture that = 14 . For triangulated...
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We deene the subvariance S P (F) of a family of graphs F with respect to property P to be the innmum of the ratio jH1j jH2j , where H 1 and H 2 are any two maximal spanning subgraphs of G with property P, and where G is a member of F. It is shown that, for the family of all connected graphs, the subvariance when P is planar, outerplanar, and bipartite planar, is 1=3, 1=2, and 1=2, respectively.
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ژورنال
عنوان ژورنال: Discrete Applied Mathematics
سال: 2016
ISSN: 0166-218X
DOI: 10.1016/j.dam.2015.06.024