Filters








201 Hits in 4.2 sec

Well Quasi Orders in Subclasses of Bounded Treewidth Graphs and Their Algorithmic Applications

Michael R. Fellows, Danny Hermelin, Frances A. Rosamond
2011 Algorithmica  
We show that three subclasses of bounded treewidth graphs are well-quasi-ordered by refinements of the minor order.  ...  Specifically, we prove that graphs with bounded vertex-covers are well quasi ordered by the induced subgraph order, graphs with bounded feedback-vertex-set are well quasi ordered by the topological-minor  ...  Our main result shows that nevertheless these orders are in fact well-quasi-orders on some natural subclasses of bounded treewidth graphs.  ... 
doi:10.1007/s00453-011-9545-y fatcat:cwobkdbqxnbwtnnc2njzm2lnci

Guest Editorial: Special Issue on Parameterized and Exact Computation, Part I

Venkatesh Raman, Saket Saurabh
2011 Algorithmica  
The paper 'Well Quasi orders in subclasses of bounded treewidth  ...  The size of the vertex cover (which measures how far the graph is from an edgeless graph) and the feedback vertex set (which measures how far the graph is from a forest) are such parameters especially  ...  The paper 'Well Quasi orders in subclasses of bounded treewidth graphs and their algorithmic applications' revisits the classical Robertson-Seymour theorem in the classes of bounded treewidth graphs that  ... 
doi:10.1007/s00453-011-9605-3 fatcat:5bwu4ykmlrcypdm5wzdvtehirq

Fast Diameter Computation within Split Graphs [article]

Guillaume Ducoffe
2021 arXiv   pre-print
We prove that it is the case for k=1 and for some subclasses such as bounded-treewidth split graphs, threshold graphs and comparability split graphs.  ...  When can we compute the diameter of a graph in quasi linear time?  ...  In Sec. 4 we prove that it is indeed the case for bounded-treewidth split graphs (trivially) and some other dense subclasses of bounded clique-interval number such as comparability split graphs.  ... 
arXiv:1910.03438v5 fatcat:kfmwqqhqe5a7blrimrt6qzgihq

Fast Diameter Computation within Split Graphs

Guillaume Ducoffe, Michel Habib, Laurent Viennot
2021 Discrete Mathematics & Theoretical Computer Science  
We prove that it is the case for $k=1$ and for some subclasses such as bounded-treewidth split graphs, threshold graphs and comparability split graphs.  ...  When can we compute the diameter of a graph in quasi linear time?  ...  In Sec. 4 we prove that it is indeed the case for bounded-treewidth split graphs (trivially) and some other dense subclasses of bounded clique-interval number such as comparability split graphs.  ... 
doi:10.46298/dmtcs.6422 fatcat:qr7voo4ic5aaddhqnd7n3w5xl4

Clique-Width for Hereditary Graph Classes [article]

Konrad K. Dabrowski, Matthew Johnson, Daniël Paulusma
2019 arXiv   pre-print
We also explain a possible strong connection between results on boundedness of clique-width and on well-quasi-orderability by the induced subgraph relation for hereditary graph classes.  ...  Clique-width is a well-studied graph parameter owing to its use in understanding algorithmic tractability: if the clique-width of a graph class G is bounded by a constant, a wide range of problems that  ...  We now present the state-of-the-art summary for well-quasi-orderability for classes on (H 1 , H 2 )-free graphs, which is obtained by combining results from [6, 63, 64, 72, 122, 123] .  ... 
arXiv:1901.00335v2 fatcat:3mb44qloc5cxxddyimwo6horqa

Beyond Outerplanarity [chapter]

Steven Chaplick, Myroslav Kryven, Giuseppe Liotta, Andre Löffler, Alexander Wolff
2018 Lecture Notes in Computer Science  
Thus, since outer k-planar graphs have bounded treewidth, closed outer k-planarity is linear-time testable by Courcelle's Theorem.  ...  For each k, we express closed outer k-planarity and closed outer k-quasi-planarity in extended monadic second-order logic.  ...  Graphs with bounded treewidth are well-known due to Courcelle's Theorem (see Theorem 6) [10] , i.e., having bounded treewidth means many problems can be solved efficiently.  ... 
doi:10.1007/978-3-319-73915-1_42 fatcat:r523bjfdojbotfnm7pxuzkmvry

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

Beyond Outerplanarity [article]

Steven Chaplick, Myroslav Kryven, Giuseppe Liotta, Andre Löffler, Alexander Wolff
2017 arXiv   pre-print
For each k, we express closed outer k-planarity and closed outer k-quasi-planarity in extended monadic second-order logic.  ...  We study straight-line drawings of graphs where the vertices are placed in convex position in the plane, i.e., convex drawings.  ...  Graphs with bounded treewidth are well-known due to Courcelle's Theorem (see Theorem 6) [10] , i.e., having bounded treewidth means many problems can be solved efficiently.  ... 
arXiv:1708.08723v2 fatcat:4bj7qcxbyfdspj4wxlinj3vs5q

On the read-once property of branching programs and CNFs of bounded treewidth [article]

Igor Razgon
2015 arXiv   pre-print
In this paper we prove a space lower bound of n^Ω(k) for non-deterministic (syntactic) read-once branching programs ( nrobps) on functions expressible as cnfs with treewidth at most k of their primal graphs  ...  We use lower bound for nrobps to obtain a quasi-polynomial separation between Free Binary Decision Diagrams and Decision Decomposable Negation Normal Forms, essentially matching the existing upper bound  ...  Oblivious ROBPs, better known as Ordered Binary Decision Diagrams (OBDDs), are a subclass of ROBPs, very well known because of its applications in the area of verification [3] .  ... 
arXiv:1411.0264v3 fatcat:p6lql42otnex3ixcvngcv3vb7y

On the Read-Once Property of Branching Programs and CNFs of Bounded Treewidth

Igor Razgon
2015 Algorithmica  
In this paper we prove a space lower bound of n Ω(k) for non-deterministic (syntactic) read-once branching programs (NROBPs) on functions expressible as CNFs with treewidth at most k of their primal graphs  ...  We use lower bound for NROBPs to obtain a quasi-polynomial separation between Free Binary Decision Diagrams and Decision Decomposable Negation Normal Forms, essentially matching the existing upper bound  ...  Oblivious ROBPs, better known as Ordered Binary Decision Diagrams (OBDDs), are a subclass of ROBPs, very well known because of its applications in the area of verification [3] .  ... 
doi:10.1007/s00453-015-0059-x fatcat:ysvytmwbp5dx5cjf3ekhlhd7li

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

Konrad K. Dabrowski, Vadim V. Lozin, Daniël Paulusma
2017 Order  
Daligault, Rao and Thomassé asked whether a hereditary class of graphs well-quasi-ordered by the induced subgraph relation has bounded clique-width.  ...  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  ...  One of the first steps towards this result was the proof of the fact that graph classes of bounded treewidth are well-quasi-ordered by the minor relation [26] (a graph parameter π is said to be bounded  ... 
doi:10.1007/s11083-017-9430-7 fatcat:setirbra4jemnp4wbxrgdcuo44

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  
In this case, the two notions even coincide: a class of graphs defined by a single forbidden induced subgraph H is well-quasi-ordered if and only if it has bounded clique-width if and only if H is an induced  ...  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  ...  One of the first steps towards this result was the proof of the fact that graph classes of bounded treewidth are well-quasi-ordered by the minor relation [26] (a graph parameter π is said to be bounded  ... 
doi:10.1007/978-3-319-44543-4_20 fatcat:row6m6uwkzdondhvk2wgkza4q4

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
Daligault, Rao and Thomassé asked whether a hereditary class of graphs well-quasi-ordered by the induced subgraph relation has bounded clique-width.  ...  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  ...  One of the first steps towards this result was the proof of the fact that graph classes of bounded treewidth are well-quasi-ordered by the minor relation [25] (a graph parameter π is said to be bounded  ... 
arXiv:1611.03671v1 fatcat:rq6a5tubgbenhhvcluolhthahq

Long induced paths in minor-closed graph classes and beyond [article]

Claire Hilaire, Jean-Florent Raymond
2022 arXiv   pre-print
In this paper we show that every graph of pathwidth less than k that has a path of order n also has an induced path of order at least 1/3 n^1/k.  ...  This result is then used to prove the two following generalizations: - every graph of treewidth less than k that has a path of order n contains an induced path of order at least 1/4 (log n)^1/k; - for  ...  Well-quasi-ordered induced subgraphs ideals. Let G be a graph class. We say that G is hereditary if any induced subgraph of a graph of G also belongs to G.  ... 
arXiv:2201.03880v1 fatcat:5bkul4kc5nfa3pvi6uvizquwey

Treewidth versus clique number. I. Graph classes with a forbidden structure [article]

Clément Dallard, Martin Milanič, Kenny Štorgel
2021 arXiv   pre-print
Treewidth is an important graph invariant, relevant for both structural and algorithmic reasons. A necessary condition for a graph class to have bounded treewidth is the absence of large cliques.  ...  In addition, we propose a question about the complexity of the maximum weight independent set problem in (tw,ω)-bounded graph classes and prove that the problem is polynomial-time solvable in every class  ...  classes, to Jean-Florent Raymond for early discussions on treewidth of 1-perfectly orientable graphs, and to Bart M.  ... 
arXiv:2006.06067v3 fatcat:v2nsvungtbht3mdplyzoecfrli
« Previous Showing results 1 — 15 out of 201 results