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Induced matchings in asteroidal triple-free graphs

2003
*
Discrete Applied Mathematics
*

The problem

doi:10.1016/s0166-218x(03)00390-1
fatcat:gtwpwwjlqbg5ldlcml4ofzitwq
*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 ). ...##
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Augmenting graphs for independent sets

2004
*
Discrete Applied Mathematics
*

We consider a general approach to solve the

doi:10.1016/j.dam.2003.09.003
fatcat:qqqm36bz2bhptblb5yj4bxmz6u
*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. ...##
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Critical properties of bipartite permutation graphs
[article]

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 |. ...

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

2012
*
Discrete Applied Mathematics
*

This yields efficient algorithms for various optimization problems

doi:10.1016/j.dam.2011.10.031
fatcat:226muztrbfhyzgchj5i2q3y6xi
*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*...##
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On the extension of bipartite to parity graphs

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*. ...

##
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On the Complexity of Dissociation Set Problems in Graphs

2009
*
IFAC Proceedings Volumes
*

The complexity

doi:10.3182/20090603-3-ru-2001.0071
fatcat:3r4kvcgpknfabmigzn3vptjd5e
*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) . ...##
###
New Graph Classes of Bounded Clique-Width
[chapter]

2002
*
Lecture Notes in Computer Science
*

Clique-width

doi:10.1007/3-540-36379-3_6
fatcat:retqdsicjfcxbhxunm2334ycoi
*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. ...##
###
New Graph Classes of Bounded Clique-Width

2004
*
Theory of Computing Systems
*

Clique-width

doi:10.1007/s00224-004-1154-6
fatcat:a3yucbewjvgejikclpwtxnym3y
*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. ...##
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Scheduling in Switching Networks with Set-Up Delays

2005
*
Journal of combinatorial optimization
*

Furthermore, we propose a simple optimal polynomial time algorithm for a

doi:10.1007/s10878-005-5483-4
fatcat:dpkl3khpx5gv7dvmfpkbwzif7i
*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 ...##
###
Statistical matching and subclassification with a continuous dose: characterization, algorithm, and application to a health outcomes study
[article]

2022
*
arXiv
*
pre-print

We discuss how to incorporate dose and use appropriate penalties to control the number

arXiv:2012.07182v2
fatcat:wkae66cnw5clpfmpnxlzacojpa
*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. ...##
###
Weighted Coloring on Planar, Bipartite and Split Graphs: Complexity and Improved Approximation
[chapter]

2004
*
Lecture Notes in Computer Science
*

We study complexity and approximation

doi:10.1007/978-3-540-30551-4_76
fatcat:w6k2px5efvfa3ebz52to4xs2zu
*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). ...##
###
Simple Games Versus Weighted Voting Games

2018
*
Social Science Research Network
*

A simple game (N, v) is given by a set N

doi:10.2139/ssrn.3174301
fatcat:uyqw3tfqsngadp2gxrpuxsofqu
*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. ...##
###
On the structure and stability number of P5- and co-chair-free graphs

2003
*
Discrete Applied Mathematics
*

We give a O(nm) time algorithm for the

doi:10.1016/s0166-218x(03)00389-5
fatcat:2ghkr2nyuvhbth7r3egfd3k62q
*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*. ...##
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The complexity of dissociation set problems in graphs

2011
*
Discrete Applied Mathematics
*

The

doi:10.1016/j.dam.2011.04.023
fatcat:nb6mvp5p2ffudhlwf5tiyeokdy
*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. ...##
###
Simple Games Versus Weighted Voting Games
[chapter]

2018
*
Lecture Notes in Computer Science
*

We also prove that for graphic simple games, that is, simple games

doi:10.1007/978-3-319-99660-8_7
fatcat:jlqbzd6p2zfd3ptzicaqrksmv4
*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. ...
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