Filters








512 Hits in 6.3 sec

Minimal dominating sets in graph classes: Combinatorial bounds and enumeration

Jean-François Couturier, Pinar Heggernes, Pim van 't Hof, Dieter Kratsch
2013 Theoretical Computer Science  
There is a graph on n vertices with 15 n/6 minimal dominating sets. This gives a lower bound of 1.5704 n for the maximum number of minimal dominating sets.  ...  This gives a lower bound of 1.5704 n for the maximum number of minimal dominating sets. Graph classes Our work is dealing with some well-known graph classes.  ... 
doi:10.1016/j.tcs.2013.03.026 fatcat:ivmx7hhl4fh6xf6ew6cdjis5ya

Enumerating minimal connected dominating sets in graphs of bounded chordality

Petr A. Golovach, Pinar Heggernes, Dieter Kratsch
2016 Theoretical Computer Science  
We establish enumeration algorithms as well as lower and upper bounds for the maximum number of minimal connected dominating sets in such graphs.  ...  In particular, we present algorithms to enumerate all minimal connected dominating sets of chordal graphs in time O(1.7159 n ), of split graphs in time O(1.3803 n ), and of AT-free, strongly chordal, and  ...  In this paper we initiate the study of the enumeration and maximum number of minimal connected dominating sets in a given graph.  ... 
doi:10.1016/j.tcs.2016.03.026 fatcat:eucvh6r4p5gl7cpvymf7qmuugu

Enumeration of Enumeration Algorithms [article]

Kunihiro Wasa
2016 arXiv   pre-print
In this paper, we enumerate enumeration problems and algorithms. This survey is under construction. If you know some results not in this survey or there is anything wrong, please let me know.  ...  Reference [115] 2.12.15 Enumeration of all minimal dominating sets in a chordal bipartite graph Input A chordal bipartite graph G. Output All minimal dominating sets in G.  ...  Reference [140] 2.12.14 Enumeration of all minimal dominating sets in a P 6 -free chordal graph Input A P 6 -free chordal graph G = (V, E). Output All minimal dominating sets in G.  ... 
arXiv:1605.05102v2 fatcat:bwmhesagkje5hmynqyij7jv224

A Note on the Maximum Number of Minimal Connected Dominating Sets in a Graph [article]

Faisal N. Abu-Khzam
2021 arXiv   pre-print
This improves the previously known lower bound of Ω(1.4422^n) and reduces the gap between lower and upper bounds for input-sensitive enumeration of minimal connected dominating sets in general graphs as  ...  We prove constructively that the maximum possible number of minimal connected dominating sets in a connected undirected graph of order n is in Ω(1.489^n).  ...  In this note we report an improved lower bound on the maximum number of minimal connected dominating sets in a graph.  ... 
arXiv:2111.06026v1 fatcat:tgatzl4b55eynhhkrhlackckya

A Polynomial Delay Algorithm for Enumerating Minimal Dominating Sets in Chordal Graphs [article]

Mamadou Moustapha Kanté and Vincent Limouzy and Arnaud Mary and Lhouari Nourine and Takeaki Uno
2014 arXiv   pre-print
We give a polynomial delay algorithm to list the set of minimal dominating sets in chordal graphs, an important and well-studied graph class where such an algorithm was open for a while.  ...  An output-polynomial algorithm for the listing of minimal dominating sets in graphs is a challenging open problem and is known to be equivalent to the well-known Transversal problem which asks for an output-polynomial  ...  For the enumeration of minimal dominating sets in chordal graphs the simplest strategy consists in following this ordering as follows.  ... 
arXiv:1407.2036v1 fatcat:wieaa7sh3zc7tjusqvvhs6ei34

A Polynomial Delay Algorithm for Enumerating Minimal Dominating Sets in Chordal Graphs [chapter]

Mamadou Moustapha Kanté, Vincent Limouzy, Arnaud Mary, Lhouari Nourine, Takeaki Uno
2016 Lecture Notes in Computer Science  
We give a polynomial delay algorithm to list the set of minimal dominating sets in chordal graphs, an important and well-studied graph class where such an algorithm was open for a while.  ...  An output-polynomial algorithm for the listing of minimal dominating sets in graphs is a challenging open problem and is known to be equivalent to the well-known Transversal problem which asks for an output-polynomial  ...  For the enumeration of minimal dominating sets in chordal graphs the simplest strategy consists in following this ordering as follows.  ... 
doi:10.1007/978-3-662-53174-7_11 fatcat:553be4juyjh67ew7zs7d5hnw44

Minimal Dominating Sets in Graph Classes: Combinatorial Bounds and Enumeration [chapter]

Jean-François Couturier, Pinar Heggernes, Pim van't Hof, Dieter Kratsch
2012 Lecture Notes in Computer Science  
For several classes of graphs, we substantially improve the upper bound on the maximum number of minimal dominating sets in graphs on n vertices.  ...  For all considered graph classes, the upper bound proofs are constructive and can easily be transformed into algorithms enumerating all minimal dominating sets of the input graph.  ...  [11] showed that all minimal dominating sets in a split graph G can be enumerated in time polynomial in the number of minimal dominating sets of G.  ... 
doi:10.1007/978-3-642-27660-6_17 fatcat:v53igxqoobbd3jmd3xxvohdsra

On the maximum number of minimal connected dominating sets in convex bipartite graphs [article]

Mohamed Yosri Sayadi
2019 arXiv   pre-print
Our algorithm implies a corresponding upper bound for the number of minimal connected dominating sets for this graph class.  ...  The enumeration of minimal connected dominating sets is known to be notoriously hard for general graphs.  ...  In this paper we study the enumeration and maximum number of minimal connected dominating sets in convex bipartite graphs, and we prove that the number of minimal connected dominating sets in a convex  ... 
arXiv:1908.02174v1 fatcat:q353hmpvovg5jeiqjbn7cdsdiu

Enumeration and maximum number of minimal connected vertex covers in graphs

Petr A. Golovach, Pinar Heggernes, Dieter Kratsch
2018 European journal of combinatorics (Print)  
For graphs of bounded chordality, we are able to give a better upper bound, and for chordal graphs and distance-hereditary graphs we are able to give tight bounds on the maximum number of minimal connected  ...  In this paper we show that the maximum number of minimal connected vertex covers of a graph is O(1.8668 n ), and these can be enumerated in time O(1.8668 n ).  ...  Examples of such recent results, both on general graphs and on some graph classes, concern the enumeration and maximum number of minimal dominating sets, minimal feedback vertex sets, minimal subset feedback  ... 
doi:10.1016/j.ejc.2017.07.015 fatcat:z7vfn6qb6jeaxjjdtwakl4oo4i

Enumeration and Maximum Number of Minimal Connected Vertex Covers in Graphs [article]

Petr A. Golovach, Pinar Heggernes, Dieter Kratsch
2016 arXiv   pre-print
For graphs of chordality at most 5, we are able to give a better upper bound, and for chordal graphs and distance-hereditary graphs we are able to give tight bounds on the maximum number of minimal connected  ...  In this paper we show that the maximum number of minimal connected vertex covers of a graph is at most 1.8668^n, and these can be enumerated in time O(1.8668^n).  ...  Examples of such recent results, both on general graphs and on some graph classes, concern the enumeration and maximum number of minimal dominating sets, minimal feedback vertex sets, minimal subset feedback  ... 
arXiv:1602.07504v1 fatcat:h5hxvzlpzzf45l42olvtxikiey

Subset feedback vertex sets in chordal graphs

Petr A. Golovach, Pinar Heggernes, Dieter Kratsch, Reza Saei
2014 Journal of Discrete Algorithms  
We give an algorithm with running time O(1.6708 n ) that enumerates all minimal subset feedback vertex sets on chordal graphs on n vertices.  ...  We also obtain that a chordal graph G has at most 1.6708 n minimal subset feedback vertex sets, regardless of S .  ...  More recently, the maximum numbers and enumeration of objects like minimal dominating sets, minimal feedback vertex sets, minimal subset feedback vertex sets, minimal separators, and potential maximal  ... 
doi:10.1016/j.jda.2013.09.005 fatcat:m74entnpo5e6vbcv55gmiudjxm

On the Neighbourhood Helly of Some Graph Classes and Applications to the Enumeration of Minimal Dominating Sets [chapter]

Mamadou Moustapha Kanté, Vincent Limouzy, Arnaud Mary, Lhouari Nourine
2012 Lecture Notes in Computer Science  
As a consequence, we obtain output-polynomial time algorithms for enumerating the set of minimal dominating sets of line graphs and path graphs.  ...  Therefore, there exists an output-polynomial time algorithm that enumerates the set of minimal edge-dominating sets of any graph.  ...  We denote by D(G) the set of (inclusionwise) minimal dominating sets of a graph G.  ... 
doi:10.1007/978-3-642-35261-4_32 fatcat:fkjgolto4rb75pxadir2i34ucy

On Distance-d Independent Set and other problems in graphs with few minimal separators [article]

Pedro Montealegre, Ioan Todinca
2016 arXiv   pre-print
We also provide polynomial algorithms for Connected Vertex Cover and Connected Feedback Vertex Set on subclasses of including chordal and circular-arc graphs, and we discuss variants of independent domination  ...  Fomin and Villanger (STACS 2010) proved that Maximum Independent Set, Feedback Vertex Set, and more generally the problem of finding a maximum induced subgraph of treewith at most a constant t, can be  ...  We thank Iyad Kanj for fruitful discussions on the subject.  ... 
arXiv:1607.04545v1 fatcat:s3y6oshzzfhhdbfnufiyv43ide

Counting the number of independent sets in chordal graphs

Yoshio Okamoto, Takeaki Uno, Ryuhei Uehara
2008 Journal of Discrete Algorithms  
We study some counting and enumeration problems for chordal graphs, especially concerning independent sets.  ...  With similar ideas, we show that enumeration (namely, listing) of the independent sets, the maximum independent sets, and the independent sets of a fixed size in a chordal graph can be done in constant  ...  Acknowledgement The authors thank Masashi Kiyomi for enlightening discussions and pointing out the work by Chang [7] . The authors are grateful to L. Shankar Ram for pointing out a paper [5] .  ... 
doi:10.1016/j.jda.2006.07.006 fatcat:pt3o77gc5zcrhdirjtbnrx5kwe

Weighted domination of independent sets [article]

Ron Aharoni, Irina Gorelik
2017 arXiv   pre-print
The independent domination number γ^i(G) of a graph G is the maximum, over all independent sets I, of the minimal number of vertices needed to dominate I.  ...  It is known abz that in chordal graphs γ^i is equal to γ, the ordinary domination number.  ...  We say that f is w-dominating if it w-dominates V . The independent domination number γ i w (G) is the maximum over all independent sets I of the minimal size of an integral function w-dominating I.  ... 
arXiv:1709.09889v1 fatcat:rgfu3beb4jeazeyaccs6ecbtsu
« Previous Showing results 1 — 15 out of 512 results