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Well-quasi-ordering H-contraction-free graphs
[article]

2016
*
arXiv
*
pre-print

More precisely, we give a complete characterization of

arXiv:1602.00733v2
fatcat:shw7ude54zcwlpdjxzizeozc5u
*graphs**H*such that the class of*H*-*contraction*-*free**graphs*is*well*-*quasi*-*ordered*by the*contraction*relation. ... This result is the*contraction*analogue on the previous dichotomy theorems of Damsaschke [Induced subgraphs and*well*-*quasi*-*ordering*, Journal of*Graph*Theory, 14(4):427-435, 1990] on the induced subgraph ... The class of*H*-subgraph-*free**graphs*is*well*-*quasi*-*ordered*by subgraphs iff*H*is a subgraph of P n , for some n ∈ N. 1 Theorem 3 ( [7] ). ...##
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Well-quasi-ordering H-contraction-free graphs

2018
*
Discrete Applied Mathematics
*

More precisely, we give a complete characterization of

doi:10.1016/j.dam.2017.02.018
fatcat:ipjb57q4hjaerbmvnraouzpiqu
*graphs**H*such that the class of*H*-*contraction*-*free**graphs*is*well*-*quasi*-*ordered*by the*contraction*relation. ... This result is the*contraction*analogue of the previous dichotomy theorems of Damsaschke [Induced subgraphs and*well*-*quasi*-*ordering*, Journal of*Graph*Theory, 14(4):427-435, 1990] on the induced subgraph ... The class of*H*-subgraph-*free**graphs*is*well*-*quasi*-*ordered*by subgraphs iff*H*is a subgraph of P n , for some n ∈ N. 1 Theorem 3 ( [7] ). ...##
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Induced minors and well-quasi-ordering
[article]

2018
*
arXiv
*
pre-print

We provide a dichotomy theorem for

arXiv:1510.07135v2
fatcat:xhajhins7nfrzazjzewonalbru
*H*-induced minor-*free**graphs*and show that the class of*H*-induced minor-*free**graphs*is*well*-*quasi*-*ordered*by the induced minor relation if and only if*H*is an induced ... Robin Thomas showed that K_4-induced minor-*free**graphs*are*well*-*quasi*-*ordered*by induced minors [*Graphs*without K_4 and*well*-*quasi*-*ordering*, Journal of Combinatorial Theory, Series B, 38(3):240 -- 247, ...*Well*-*quasi*-*ordering*Gem-induced minor-*free**graphs*In this section we give a proof of Theorem 5. ...##
###
Page 1230 of Mathematical Reviews Vol. 45, Issue 5
[page]

1973
*
Mathematical Reviews
*

Soc. 95 (1960), 210-225; MR 22 #2566] that the class of

*graphs*in which the degrees of all vertices are <3 is*well*-*quasi*-*ordered*by <. C. St. J. A. ... It is also proved that, for each positive integer n, the class of all finite*graphs*which do not contain n disjoint circuits is*well*-*quasi*-*ordered*by <. ...##
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Induced minors and well-quasi-ordering

2015
*
Electronic Notes in Discrete Mathematics
*

We provide a dichotomy theorem for

doi:10.1016/j.endm.2015.06.029
fatcat:duodehjj3ra6piwmkovtuaxmci
*H*-induced minor-*free**graphs*and show that the class of*H*-induced minor-*free**graphs*is*well*-*quasi*-*ordered*by the induced minor relation if and only if*H*is an induced ... Robin Thomas showed that K 4 -induced minor-*free**graphs*are*well*-*quasi*-*ordered*by induced minors [*Graphs*without K 4 and*well*-*quasi*-*ordering*, Journal of Combinatorial Theory, Series B, 38 (3) : 240 -247 ...*Well*-*quasi*-*ordering*Gem-induced minor-*free**graphs*In this section we will give a proof of Theorem 5. ...##
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A decidability result for the dominating set problem

2010
*
Theoretical Computer Science
*

We study the following question: given a finite collection of

doi:10.1016/j.tcs.2010.08.027
fatcat:t4txbi55efa43ba2usf33rjd5y
*graphs*G 1 , . . . , G k , is the dominating set problem polynomial-time solvable in the class of (G 1 , . . . , G k )-*free**graphs*? ... To see that Q is*well*-*quasi*-*ordered*, observe that a*graph*G ∈ S is an induced subgraph of the*graph**H*∈ S if and only if G * ∈ Q is an induced subgraph of*H** ∈ Q. ... Therefore, T is also*well*-*quasi*-*ordered*by induced subgraphs. ...##
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Bipartite Induced Subgraphs and Well-Quasi-Ordering
[article]

2010
*
arXiv
*
pre-print

We study bipartite

arXiv:1005.1328v1
fatcat:o65wexlrizbadm34erf6t4nhgi
*graphs*partially*ordered*by the induced subgraph relation. Our goal is to distinguish classes of bipartite*graphs*which are or are not*well*-*quasi*-*ordered*(wqo) by this relation. ... Answering an open question from Ding92, we prove that P_7-*free*bipartite*graphs*are not wqo. On the other hand, we show that P_6-*free*bipartite*graphs*are wqo. ... Not*well*-*quasi*-*ordered*classes of bipartite*graphs*In [3] , Ding proved that the class of (P 8 , P 8 )-*free*bipartite*graphs*is not*well*-*quasi*-*ordered*by the induced subgraph relation. ...##
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Well-Quasi-Ordering versus Clique-Width: New Results on Bigenic Classes

2017
*
Order
*

The conjecture is known to hold for classes of

doi:10.1007/s11083-017-9430-7
fatcat:setirbra4jemnp4wbxrgdcuo44
*graphs*defined by a single forbidden induced subgraph*H*, as such*graphs*are*well*-*quasi*-*ordered*and are of bounded clique-width if and only if*H*is an induced ... 2017) '*Well*-*quasi*-*ordering*versus clique-width : new results on bigenic classes. ... Two New Non-*Well*-*Quasi*-*Ordered*Classes In this section we show that the classes of (2P 1 + P 2 , P 2 + P 4 )-*free**graphs*and (P 1 + P 4 , P 1 +2P 2 )-*free**graphs*are not*well*-*quasi*-*ordered*by the induced ...##
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Two forbidden induced subgraphs and well-quasi-ordering

2011
*
Discrete Mathematics
*

A set of

doi:10.1016/j.disc.2011.04.023
fatcat:bq6wz72lgrfrvpth4xkatbi5am
*graphs*X is*well*-*quasi*-*ordered*(by the induced subgraph relation) if and only if connected*graphs*in X are*well*-*quasi*-*ordered*. ... However, very little is known about*well*-*quasi*-*ordered*classes of*graphs*defined by more than one forbidden induced subgraph. ... Bigenic classes of*graphs*which are*well*-*quasi*-*ordered*In this section, we reveal a number of bigenic classes which are*well*-*quasi*-*ordered*by induced subgraphs. ...##
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Well-Quasi-Ordering versus Clique-Width: New Results on Bigenic Classes
[chapter]

2016
*
Lecture Notes in Computer Science
*

Since then, Atminas and Lozin [1] proved that the class of (K 3 , P 6 )-

doi:10.1007/978-3-319-44543-4_20
fatcat:row6m6uwkzdondhvk2wgkza4q4
*free**graphs*is*well*-*quasi*-*ordered*by the induced subgraph relation and that the class of (2P 1 + P 2 , P 6 )-*free**graphs*is not. ... Very recently, we used the techniques developed in the present paper to prove that the classes of (P 1 + P 3 , P 2 + P 4 )*free**graphs*and (P 1 + P 3 , P 1 + P 5 )-*free**graphs*are also*well*-*quasi*-*ordered*...*Well*-*Quasi*-*Ordering*Atminas and Lozin [1] proved that the class of (K 3 , P 6 )-*free**graphs*is*well*-*quasi*-*ordered*by the induced subgraph relation, while the class of (2P 1 + P 2 , P 6 )-*free**graphs*...##
###
Page 5449 of Mathematical Reviews Vol. , Issue 86m
[page]

1986
*
Mathematical Reviews
*

that the class of planar

*graphs*is not*well*-*quasi*-*ordered*by <. ... Carsten Thomassen (Copenhagen) 86m:05075 Thomas, Robin (CS-CHRL)*Graphs*without K, and*well*-*quasi*-*ordering*. J. Combin. Theory Ser. B 38 (1985), no. 3, 240-247. ...##
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Well-Quasi-Ordering versus Clique-Width: New Results on Bigenic Classes
[article]

2016
*
arXiv
*
pre-print

The conjecture is known to hold for classes of

arXiv:1611.03671v1
fatcat:rq6a5tubgbenhhvcluolhthahq
*graphs*defined by a single forbidden induced subgraph*H*, as such*graphs*are*well*-*quasi*-*ordered*and are of bounded clique-width if and only if*H*is an induced ... Daligault, Rao and Thomassé asked whether a hereditary class of*graphs**well*-*quasi*-*ordered*by the induced subgraph relation has bounded clique-width. ... Open Problem 1 Is the class of (*H*1 ,*H*2 )-*free**graphs**well*-*quasi*-*ordered*by the induced subgraph relation when: (i)*H*1 = 3P 1 and*H*2 ∈ {P 1 + 2P 2 , P 1 + P 5 , P 2 + P 4 }; (ii)*H*1 = 2P 1 + P 2 and ...##
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Graphs without large bicliques and well-quasi-orderability by the induced subgraph relation
[article]

2015
*
arXiv
*
pre-print

Recently, Daligault, Rao and Thomass\'e asked in [3] if every hereditary class which is

arXiv:1410.3260v2
fatcat:kjo6xlckn5hjdiegokkvbjkhoa
*well*-*quasi*-*ordered*by the induced subgraph relation is of bounded clique-width. ... In particular, this will mean (through the use of Courcelle theorem [2]), that any problem definable in Monadic Second*Order*Logic can be solved in a polynomial time on any class*well*-*quasi*-*ordered*by ... If X is a hereditary subclass of (K t , K q,q )-*free**graphs*which is*well*-*quasi*-*ordered*by the induced subgraph relation, then X has a bounded treewidth. ...##
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Clique-Width and Well-Quasi-Ordering of Triangle-Free Graph Classes
[chapter]

2017
*
Lecture Notes in Computer Science
*

In both of 1 We refer to [5, 20, 30] for classifications of

doi:10.1007/978-3-319-68705-6_17
fatcat:4wzezy3qvfbadh3ihj7hsfvqde
*well*-*quasi*-*orderability*by the induced-minor, subgraph and*contraction*relations, respectively, for classes of*H*-*free**graphs*. ... We obtain a complete classification of*graphs**H*for which the class of (triangle,*H*)-*free**graphs*is*well*-*quasi*-*ordered*by the induced subgraph relation and an almost complete classification of*graphs**H*... Let*H*be a*graph*. The class of*H*-*free*bipartite*graphs*is*well*-*quasi*-*ordered*by the induced subgraph relation if and only if*H*= sP Theorem 2. Let*H*be a*graph*. ...##
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On the Decidability Status of Reachability and Coverability in Graph Transformation Systems

2012
*
International Conference on Rewriting Techniques and Applications
*

In this paper we reformulate results obtained, e.g., for context-

doi:10.4230/lipics.rta.2012.101
dblp:conf/rta/BertrandDKSS12
fatcat:62mssb5jebadxaiw7ojdlp2c7e
*free**graph*grammars and concurrency models, such as Petri nets, in the more general setting of*graph*transformation systems and study new ... We study decidability issues for reachability problems in*graph*transformation systems, a powerful infinite-state model. ... We prove*well*-structuredness of GTS with*contraction*rules for all possible edge labels. We first recall that the*graph*minor*ordering*is a decidable*well*-*quasi**ordering*[22] . ...
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