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Induced matchings in asteroidal triple-free graphs

Jou-Ming Chang
2003 Discrete Applied Mathematics  
The problem of ÿnding a maximum induced matching is known to be NP-hard even for bipartite graphs of maximum degree four.  ...  In this paper, we study the maximum induced matching problem on classes of graphs related to AT-free graphs.  ...  The maximum induced matching problem is that of ÿnding an induced matching with the maximum cardinality in a graph G (see Fig. 1 ).  ... 
doi:10.1016/s0166-218x(03)00390-1 fatcat:gtwpwwjlqbg5ldlcml4ofzitwq

Augmenting graphs for independent sets

Vladimir E. Alekseev, Vadim V. Lozin
2004 Discrete Applied Mathematics  
We consider a general approach to solve the maximum independent set problem based on ÿnding augmenting graphs. For some special classes of graphs, the approach provides polynomial solutions.  ...  We also discuss some open questions related to the notion of augmenting graphs.  ...  Obviously, the independent set problem in L is equivalent to the problem of ÿnding a maximum matching (independent set of edges) in graph G.  ... 
doi:10.1016/j.dam.2003.09.003 fatcat:qqqm36bz2bhptblb5yj4bxmz6u

Critical properties of bipartite permutation graphs [article]

Bogdan Alecu, Vadim Lozin, Dmitriy Malyshev
2020 arXiv   pre-print
In the present paper we identify critical subclasses of bipartite permutation graphs of various types.  ...  The class of bipartite permutation graphs enjoys many nice and important properties.  ...  We reduce the problem to finding a maximum weight one-sided-perfect matching in an auxiliary edge-weighted complete bipartite graph B with order linear in |V G |.  ... 
arXiv:2010.14467v1 fatcat:4limdlsygvdatfeyksncg3bm2u

Clique separator decomposition of hole-free and diamond-free graphs and algorithmic consequences

Andreas Brandstädt, Vassilis Giakoumakis, Frédéric Maffray
2012 Discrete Applied Mathematics  
This yields efficient algorithms for various optimization problems in this class of graphs.  ...  We show that every (hole, paraglider)-free graph admits a clique separator decomposition into graphs of three very specific types.  ...  In a complete multipartite graph there is no induced matching of size 2, and in a matched co-bipartite graph there is no induced matching of size 3, so in either class the search for a maximum weight induced  ... 
doi:10.1016/j.dam.2011.10.031 fatcat:226muztrbfhyzgchj5i2q3y6xi

On the extension of bipartite to parity graphs

Serafino Cicerone, Gabriele Di Stefano
1999 Discrete Applied Mathematics  
maximum weighted clique.  ...  Parity graphs form a superclass of bipartite and distance-hereditary graphs.  ...  Each deÿned class di ers from the others in that adds graphs belonging to a speciÿc subclass of bipartite graphs.  ... 
doi:10.1016/s0166-218x(99)00074-8 fatcat:wak4akrenzf3lms5pcm32xwphy

On the Complexity of Dissociation Set Problems in Graphs

Yury Orlovich, Alexandre Dolgui, Gerd Finke, Valery Gordon, Frank Werner
2009 IFAC Proceedings Volumes  
The complexity of finding a dissociation set of maximum size in line graphs and finding a maximal dissociation set of minimum size in general graphs is considered.  ...  A subset of vertices in a graph is called a dissociation set if it induces a subgraph with vertex degree at most 1. A dissociation set D is maximal if no other dissociation set contains D.  ...  The maximum cardinality of an induced matching of G is the induced matching number, and it is denoted by ) (G Σ . Brandstädt et al., (1999) .  ... 
doi:10.3182/20090603-3-ru-2001.0071 fatcat:3r4kvcgpknfabmigzn3vptjd5e

New Graph Classes of Bounded Clique-Width [chapter]

Andreas Brandstädt, Feodor F. Dragan, Hoàng-Oanh Le, Raffaele Mosca
2002 Lecture Notes in Computer Science  
Clique-width of graphs is a major new concept with respect to efficiency of graph algorithms; it is known that every algorithmic problem expressible in a certain kind of Monadic Second Order Logic called  ...  LinEMSOL(τ1,L) by Courcelle, Makowsky and Rotics, is solvable in linear time on any graph class with bounded clique-width for which a k-expression for the input graph can be constructed in linear time  ...  The problems Vertex Cover, Maximum Weight Stable Set (MWS), Maximum Weight Clique, Steiner Tree and Domination are examples of LinEMSOL(τ 1,L ) definable problems.  ... 
doi:10.1007/3-540-36379-3_6 fatcat:retqdsicjfcxbhxunm2334ycoi

New Graph Classes of Bounded Clique-Width

Andreas Brandstädt, Feodor F. Dragan, Hoàng-Oanh Le, Raffaele Mosca
2004 Theory of Computing Systems  
Clique-width of graphs is a major new concept with respect to efficiency of graph algorithms; it is known that every algorithmic problem expressible in a certain kind of Monadic Second Order Logic called  ...  LinEMSOL(τ1,L) by Courcelle, Makowsky and Rotics, is solvable in linear time on any graph class with bounded clique-width for which a k-expression for the input graph can be constructed in linear time  ...  The problems Vertex Cover, Maximum Weight Stable Set (MWS), Maximum Weight Clique, Steiner Tree and Domination are examples of LinEMSOL(τ 1,L ) definable problems.  ... 
doi:10.1007/s00224-004-1154-6 fatcat:a3yucbewjvgejikclpwtxnym3y

Scheduling in Switching Networks with Set-Up Delays

Foto Afrati, Timos Aslanidis, Evripidis Bampis, Ioannis Milis
2005 Journal of combinatorial optimization  
Furthermore, we propose a simple optimal polynomial time algorithm for a subclass of instances of the PBS problem.  ...  We consider the (preemptive bipartite scheduling problem PBS) (Crescenzi et al., "On approximating a scheduling problem," Journal of Combinatorial Optimization, vol. 5, pp. 287-297, 2001) arising in switching  ...  A class of graphs with polynomial solution to the problem In this section we present a polynomial time algorithm for the PBS problem when restricted to a subclass of weighted bipartite graphs, that we  ... 
doi:10.1007/s10878-005-5483-4 fatcat:dpkl3khpx5gv7dvmfpkbwzif7i

Statistical matching and subclassification with a continuous dose: characterization, algorithm, and application to a health outcomes study [article]

Bo Zhang, Emily J. Mackay, Mike Baiocchi
2022 arXiv   pre-print
We discuss how to incorporate dose and use appropriate penalties to control the number of subclasses in the design.  ...  In this article, we propose two criteria for optimal subclassification based on subclass homogeneity in the context of having a continuous exposure dose, and propose an efficient polynomial-time algorithm  ...  In the context of non-bipartite matching with a continuous dose, we may also want to have some control over the size of subclasses and hence how many subclasses in a subclassification.  ... 
arXiv:2012.07182v2 fatcat:wkae66cnw5clpfmpnxlzacojpa

Weighted Coloring on Planar, Bipartite and Split Graphs: Complexity and Improved Approximation [chapter]

Dominique de Werra, Mare Demange, Bruno Escoffier, Jerome Monnot, Vangelis Th. Paschos
2004 Lecture Notes in Computer Science  
We study complexity and approximation of min weighted node coloring in planar, bipartite and split graphs.  ...  Then, we prove that min weighted node coloring is NP-complete in P8-free bipartite graphs, but polynomial for P5-free bipartite graphs.  ...  to the node-model, the weight of a matching is the maximum of the weights of its edges).  ... 
doi:10.1007/978-3-540-30551-4_76 fatcat:w6k2px5efvfa3ebz52to4xs2zu

Simple Games Versus Weighted Voting Games

Frits Hof, Walter Kern, Sascha Kurz, Daniil Paulusma
2018 Social Science Research Network  
A simple game (N, v) is given by a set N of n players and a partition of 2 N into a set L of losing coalitions L with value v(L) = 0 that is closed under taking subsets and a set W of winning coalitions  ...  The second and fourth author thank Péter Biró and Hajo Broersma for fruitful discussions on the topic of the paper.  ...  In the corresponding matching game a coalition S ⊆ N has value v(S) equal to the maximum size of a matching in the subgraph of G induced by S.  ... 
doi:10.2139/ssrn.3174301 fatcat:uyqw3tfqsngadp2gxrpuxsofqu

On the structure and stability number of P5- and co-chair-free graphs

Andreas Brandstädt, Raffaele Mosca
2003 Discrete Applied Mathematics  
We give a O(nm) time algorithm for the maximum weight stable set (MWS) problem on P5-and co-chair-free graphs without recognizing whether the (arbitrary) input graph is P5and co-chair-free.  ...  This algorithm is based on the fact that prime P5-and co-chair-free graphs containing 2K2 are matched co-bipartite graphs and thus have very simple structure, and for 2K2-free graphs, there is a polynomial  ...  The Maximum (Weight) Stable Set (M (W )S) Problem asks for a maximum (vertex weight) stable set in the given graph.  ... 
doi:10.1016/s0166-218x(03)00389-5 fatcat:2ghkr2nyuvhbth7r3egfd3k62q

The complexity of dissociation set problems in graphs

Yury Orlovich, Alexandre Dolgui, Gerd Finke, Valery Gordon, Frank Werner
2011 Discrete Applied Mathematics  
The maximum dissociation set problem, i.e., the problem of finding a dissociation set of maximum size in a given graph is known to be NP-hard for bipartite graphs.  ...  A subset of vertices in a graph is called a dissociation set if it induces a subgraph with a vertex degree of at most 1.  ...  The first author's research was also partially supported by grant No. 478/39 of the Ministry of Education of the Republic of Belarus.  ... 
doi:10.1016/j.dam.2011.04.023 fatcat:nb6mvp5p2ffudhlwf5tiyeokdy

Simple Games Versus Weighted Voting Games [chapter]

Frits Hof, Walter Kern, Sascha Kurz, Daniël Paulusma
2018 Lecture Notes in Computer Science  
We also prove that for graphic simple games, that is, simple games in which every minimal winning coalition has size 2, computing α is -hard, but polynomial-time solvable if the underlying graph is bipartite  ...  A simple game (N,v) is given by a set N of n players and a partition of 2^N into a set L of losing coalitions L with value v(L)=0 that is closed under taking subsets and a set W of winning coalitions W  ...  The second and fourth author thank Péter Biró and Hajo Broersma for fruitful discussions on the topic of the paper.  ... 
doi:10.1007/978-3-319-99660-8_7 fatcat:jlqbzd6p2zfd3ptzicaqrksmv4
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