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Dominating induced matchings and other graph parameters
AKCE International Journal of Graphs and CombinatoricsA matching M in a graph G is an induced matching if the largest degree of the subgraph of G induced by M is equal to one. A dominating induced matching (DIM) of G is an induced matching that dominates every edge of G. It is well known that, if they exist,
A. Mahmoodi +3 more
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Dominating Induced Matchings in $S_{1,2,4}$-Free Graphs [PDF]
Discrete Applied Mathematics, 2017 Let $G=(V,E)$ be a finite undirected graph without loops and multiple edges. A subset $M \subseteq E$ of edges is a {\em dominating induced matching} ({\em d.i.m.}) in $G$ if every edge in $E$ is intersected by exactly one edge of $M$. In particular, this means that $M$ is an induced matching, and every edge not in $M$ shares exactly one vertex with an
Andreas Brandstädt, Raffaele Mosca
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Some Results on Dominating Induced Matchings
Graphs and Combinatorics, 2022 Let $G$ be a graph, a dominating induced matching (DIM) of $G$ is an induced matching that dominates every edge of $G$. In this paper we show that if a graph $G$ has a DIM, then $ (G) \leqslant 3$. Also, it is shown that if $G$ is a connected graph whose all edges can be partitioned into DIM, then $G$ is either a regular graph or a biregular graph and
S. Akbari +4 more
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Dominating Induced Matchings for P 7-free Graphs in Linear Time [PDF]
Algorithmica, 2011 Let $G$ be a finite undirected graph with edge set $E$. An edge set $E' \subseteq E$ is an {\em induced matching} in $G$ if the pairwise distance of the edges of $E'$ in $G$ is at least two; $E'$ is {\em dominating} in $G$ if every edge $e \in E \setminus E'$ intersects some edge in $E'$.
Brandstädt, Andreas, Mosca, Raffaele
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Paired and induced-paired domination in (E,net)-free graphs [PDF]
, 2011 A dominating set of a graph is a vertex subset that any vertex belongs to or is adjacent to. Among the many well-studied variants of domination are the so-called paired-dominating sets.
Schaudt, Oliver
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More Applications of the d-Neighbor Equivalence: Connectivity and Acyclicity Constraints [PDF]
, 2019 In this paper, we design a framework to obtain efficient algorithms for several problems with a global constraint (acyclicity or connectivity) such as Connected Dominating Set, Node Weighted Steiner Tree, Maximum Induced Tree, Longest Induced Path, and ...
Bergougnoux, Benjamin +1 more
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The Maximum Number of Dominating Induced Matchings
Journal of Graph Theory, 2014 AbstractA matching M of a graph G is a dominating induced matching (DIM) of G if every edge of G is either in M or adjacent with exactly one edge in M. We prove sharp upper bounds on the number of DIMs of a graph G and characterize all extremal graphs.
Lin, Min Chih +3 more
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Finding dominating induced matchings in P10-free graphs in polynomial time
Theoretical Computer Science, 2022 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Brandstädt, Andreas, Mosca, Raffaele
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Dominating induced matchings in graphs containing no long claw [PDF]
Journal of Graph Theory, 2017 AbstractAn induced matching M in a graph G is dominating if every edge not in M shares exactly one vertex with an edge in M. The dominating induced matching problem (also known as efficient edge domination) asks whether a graph G contains a dominating induced matching.
Alain Hertz +4 more
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Efficient and Perfect domination on circular-arc graphs [PDF]
, 2015 Given a graph $G = (V,E)$, a \emph{perfect dominating set} is a subset of vertices $V' \subseteq V(G)$ such that each vertex $v \in V(G)\setminus V'$ is dominated by exactly one vertex $v' \in V'$.
Lin, Min Chih +2 more
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