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On the approximability of the maximum induced matching problem
 Journal of Discrete Algorithms
, 2005
"... In this paper we consider the approximability of the maximum induced matching problem (MIM). We give an approximation algorithm with asymptotic performance ratio d − 1 for MIM in dregular graphs, for each d ≥ 3. We also prove that MIM is APXcomplete in dregular graphs, for each d ≥ 3. ..."
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Cited by 20 (3 self)
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In this paper we consider the approximability of the maximum induced matching problem (MIM). We give an approximation algorithm with asymptotic performance ratio d − 1 for MIM in dregular graphs, for each d ≥ 3. We also prove that MIM is APXcomplete in dregular graphs, for each d ≥ 3.
A Polynomial Algorithm to Find an Independent Set of Maximum Weight in a Forkfree Graph
, 2005
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On Minimal Prime Extensions of a FourVertex Graph in a Prime Graph
, 2002
"... In a finite undirected graph G = (V; E), a homogeneous set is a set U V of at least two vertices such that every vertex in V n U is either adjacent to all vertices of U or nonadjacent to all of them. A graph is prime if it does not have a homogeneous set. We investigate the minimum... ..."
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Cited by 6 (1 self)
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In a finite undirected graph G = (V; E), a homogeneous set is a set U V of at least two vertices such that every vertex in V n U is either adjacent to all vertices of U or nonadjacent to all of them. A graph is prime if it does not have a homogeneous set. We investigate the minimum...
New Graph Classes of Bounded CliqueWidth
, 2003
"... Cliquewidth of graphs is a major new concept with respect to efficiency of graph algorithms; it is known that every problem expressible in a certain kind of Monadic Second Order Logic called LinEMSOL(τ1,L ) by Courcelle, Makowsky and Rotics, is lineartime solvable on any graph class with bounded c ..."
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Cited by 5 (0 self)
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Cliquewidth of graphs is a major new concept with respect to efficiency of graph algorithms; it is known that every problem expressible in a certain kind of Monadic Second Order Logic called LinEMSOL(τ1,L ) by Courcelle, Makowsky and Rotics, is lineartime solvable on any graph class with bounded cliquewidth for which a kexpression for the input graph can be constructed in linear time. The notion of cliquewidth...
New Applications of Clique Separator Decomposition for the Maximum Weight Stable Set problem
, 2007
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Efficient Robust Algorithms for the Maximum Weight Stable Set Problem in Chairfree Graph Classes
, 2001
"... Modular decomposition of graphs is a powerful tool for designing efficient algorithms for algorithmic graph problems such as the Maximum Weight Stable Set Problem and the Maximum Weight Clique Problem. Using this tool we obtain O(nm) time algorithms for the Maximum Weight Stable Set Problem on (chai ..."
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Cited by 3 (1 self)
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Modular decomposition of graphs is a powerful tool for designing efficient algorithms for algorithmic graph problems such as the Maximum Weight Stable Set Problem and the Maximum Weight Clique Problem. Using this tool we obtain O(nm) time algorithms for the Maximum Weight Stable Set Problem on (chair, coP)free, (chair,P5)free and (chair,bull)free graphs. Moreover, our algorithms are robust in the sense that we do not have to check in advance whether the input graphs are indeed (chair, coP)free or (chair,P5)free or (chair,bull)free.
Induced matchings and induced paths in graphs
 UNPUBLISHED MANUSCRIPT, KAMDIMATIA SERIES
, 2007
"... Denote by ∇1(G) the maximum of E(H) over all (simple) minors V (H) of G obtained by contracting a star forest. We prove that there exists a positive function ǫ such that every graph G of order n has (at least) two clones (that is two vertices with the same neighbours) or an induced matching of ..."
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Denote by ∇1(G) the maximum of E(H) over all (simple) minors V (H) of G obtained by contracting a star forest. We prove that there exists a positive function ǫ such that every graph G of order n has (at least) two clones (that is two vertices with the same neighbours) or an induced matching of size at least ǫ(∇1(G))n and that this set may be found in linear time. More generally, we prove that for every integer k there exists a (very slowly growing) positive function ǫk such that every graph of order n has an involutive automorphism or includes a set of size at least k⌊ǫk(∇⌊k/2⌋(G))n ⌋ inducing ⌊ǫk(∇⌊k/2⌋(G))n ⌋ disjoint paths on k vertices.
Laboratoire d'Analyse et Modélisation de Systèmes pour l'Aide à la Décision
"... Some tractable instances of interval data minmax regret problems: bounded distance from triviality ..."
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Some tractable instances of interval data minmax regret problems: bounded distance from triviality