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

Marcin Kamiński, Jean-Florent Raymond, Théophile Trunck
2016 arXiv   pre-print
More precisely, we give a complete characterization of 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] ).  ... 
arXiv:1602.00733v2 fatcat:shw7ude54zcwlpdjxzizeozc5u

Well-quasi-ordering H-contraction-free graphs

Marcin Kamiński, Jean-Florent Raymond, Théophile Trunck
2018 Discrete Applied Mathematics  
More precisely, we give a complete characterization of 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] ).  ... 
doi:10.1016/j.dam.2017.02.018 fatcat:ipjb57q4hjaerbmvnraouzpiqu

Induced minors and well-quasi-ordering [article]

Jarosław Błasiok, Marcin Kamiński, Jean-Florent Raymond, and Théophile Trunck
2018 arXiv   pre-print
We provide a dichotomy theorem for 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.  ... 
arXiv:1510.07135v2 fatcat:xhajhins7nfrzazjzewonalbru

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 <.  ... 

Induced minors and well-quasi-ordering

Jarosław Błasiok, Marcin Kamiński, Jean-Florent Raymond, Théophile Trunck
2015 Electronic Notes in Discrete Mathematics  
We provide a dichotomy theorem for 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.  ... 
doi:10.1016/j.endm.2015.06.029 fatcat:duodehjj3ra6piwmkovtuaxmci

A decidability result for the dominating set problem

Vadim V. Lozin
2010 Theoretical Computer Science  
We study the following question: given a finite collection of 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.  ... 
doi:10.1016/j.tcs.2010.08.027 fatcat:t4txbi55efa43ba2usf33rjd5y

Bipartite Induced Subgraphs and Well-Quasi-Ordering [article]

Nicholas Korpelainen, Vadim V. Lozin
2010 arXiv   pre-print
We study bipartite 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.  ... 
arXiv:1005.1328v1 fatcat:o65wexlrizbadm34erf6t4nhgi

Well-Quasi-Ordering versus Clique-Width: New Results on Bigenic Classes

Konrad K. Dabrowski, Vadim V. Lozin, Daniël Paulusma
2017 Order  
The conjecture is known to hold for classes of 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  ... 
doi:10.1007/s11083-017-9430-7 fatcat:setirbra4jemnp4wbxrgdcuo44

Two forbidden induced subgraphs and well-quasi-ordering

Nicholas Korpelainen, Vadim Lozin
2011 Discrete Mathematics  
A set of 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.  ... 
doi:10.1016/j.disc.2011.04.023 fatcat:bq6wz72lgrfrvpth4xkatbi5am

Well-Quasi-Ordering versus Clique-Width: New Results on Bigenic Classes [chapter]

Konrad K. Dabrowski, Vadim V. Lozin, Daniël Paulusma
2016 Lecture Notes in Computer Science  
Since then, Atminas and Lozin [1] proved that the class of (K 3 , P 6 )-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  ... 
doi:10.1007/978-3-319-44543-4_20 fatcat:row6m6uwkzdondhvk2wgkza4q4

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.  ... 

Well-Quasi-Ordering versus Clique-Width: New Results on Bigenic Classes [article]

Konrad K. Dabrowski and Vadim V. Lozin and Daniël Paulusma
2016 arXiv   pre-print
The conjecture is known to hold for classes of 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  ... 
arXiv:1611.03671v1 fatcat:rq6a5tubgbenhhvcluolhthahq

Graphs without large bicliques and well-quasi-orderability by the induced subgraph relation [article]

Aistis Atminas, Vadim V. Lozin, Igor Razgon
2015 arXiv   pre-print
Recently, Daligault, Rao and Thomass\'e asked in [3] if every hereditary class which is 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.  ... 
arXiv:1410.3260v2 fatcat:kjo6xlckn5hjdiegokkvbjkhoa

Clique-Width and Well-Quasi-Ordering of Triangle-Free Graph Classes [chapter]

Konrad K. Dabrowski, Vadim V. Lozin, Daniël Paulusma
2017 Lecture Notes in Computer Science  
In both of 1 We refer to [5, 20, 30] for classifications of 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.  ... 
doi:10.1007/978-3-319-68705-6_17 fatcat:4wzezy3qvfbadh3ihj7hsfvqde

On the Decidability Status of Reachability and Coverability in Graph Transformation Systems

Nathalie Bertrand, Giorgio Delzanno, Barbara König, Arnaud Sangnier, Jan Stückrath, Marc Herbstritt
2012 International Conference on Rewriting Techniques and Applications  
In this paper we reformulate results obtained, e.g., for context-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] .  ... 
doi:10.4230/lipics.rta.2012.101 dblp:conf/rta/BertrandDKSS12 fatcat:62mssb5jebadxaiw7ojdlp2c7e
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