Independence and Efficient Domination on P 6 -free Graphs
نویسندگان
چکیده
منابع مشابه
Independence and Efficient Domination on P6-free Graph
In the Maximum Weight Independent Set problem, the input is a graph G, every vertex has a non-negative integer weight, and the task is to find a set S of pairwise non-adjacent vertices, maximizing the total weight of the vertices in S. We give an nO(log 2 n) time algorithm for this problem on graphs excluding the path P6 on 6 vertices as an induced subgraph. Currently, there is no constant k kn...
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In a graph G, an efficient dominating set is a subset D of vertices such that D is an independent set and each vertex outside D has exactly one neighbor in D. The Efficient Dominating Set problem (EDS) asks for the existence of an efficient dominating set in a given graph G. The EDS is known to be NP -complete for P7-free graphs, and is known to be polynomial time solvable for P5-free graphs. H...
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Vizing’s conjecture is true for graphs G satisfying γ(G) = γ(G), where γ(G) is the domination number of a graph G and γ(G) is the independence-domination number of G, that is, the maximum, over all independent sets I in G, of the minimum number of vertices needed to dominate I . The equality γ(G) = γ(G) is known to hold for all chordal graphs and for chordless cycles of length 0 (mod 3). We pro...
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A set S of vertices in a graph G is a paired-dominating set of G if every vertex of G is adjacent to some vertex in S and if the subgraph induced by S contains a perfect matching. The paired-domination number of G, denoted by γpr(G), is the minimum cardinality of a paired-dominating set of G. In [?], the authors gave tight bounds for paired-dominating sets of generalized claw-free graphs. Yet, ...
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A graph $G$ is called $P_4$-free, if $G$ does not contain an induced subgraph $P_4$. The domination polynomial of a graph $G$ of order $n$ is the polynomial $D(G,x)=sum_{i=1}^{n} d(G,i) x^{i}$, where $d(G,i)$ is the number of dominating sets of $G$ of size $i$. Every root of $D(G,x)$ is called a domination root of $G$. In this paper we state and prove formula for the domination polynomial of no...
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ژورنال
عنوان ژورنال: ACM Transactions on Algorithms
سال: 2018
ISSN: 1549-6325,1549-6333
DOI: 10.1145/3147214