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A linear-time algorithm for semitotal domination in strongly chordal graphs [article]

Vikash Tripathi, Arti Pandey, Anil Maheshwari
2021 arXiv   pre-print
In this paper, we resolve the complexity of the problem in strongly chordal graphs by designing a linear-time algorithm for the problem.  ...  In a graph G=(V,E) with no isolated vertex, a dominating set D ⊆ V, is called a semitotal dominating set if for every vertex u ∈ D there is another vertex v ∈ D, such that distance between u and v is at  ...  Algorithm for Semitotal Domination in Strongly Chordal Graphs In this section, we propose, a linear-time algorithm to compute a minimum semi-TD-set in strongly chordal graphs.  ... 
arXiv:2109.02142v1 fatcat:fssjv6dw4rc2jph3ynrvadzkpu

Algorithmic Aspects of Semitotal Domination in Graphs [article]

Michael A. Henning, Arti Pandey
2017 arXiv   pre-print
We give a polynomial time algorithm to solve the Minimum Semitotal Domination problem in interval graphs.  ...  In this paper, we show that the Semitotal Domination Decision problem remains NP-complete for planar graphs, split graphs and chordal bipartite graphs.  ...  It will be interesting to look for the complexity status of the problem for strongly chordal graphs, which is a subclass of chordal graphs, but superclass of interval graphs.  ... 
arXiv:1711.10891v1 fatcat:tash2wg3lzekbip73tqaarfeim

Semitotal Domination: New hardness results and a polynomial-time algorithm for graphs of bounded mim-width

Esther Galby, Andrea Munaro, Bernard Ries
2020 Theoretical Computer Science  
In particular, we show that it is solvable in polynomial time for the class of graphs of bounded mim-width by a reduction to TOTAL DOMINATING SET and we provide several approximation lower bounds for subclasses  ...  A semitotal dominating set of a graph G with no isolated vertex is a dominating set D of G such that every vertex in D is within distance two of another vertex in D.  ...  Acknowledgments We would like to thank the anonymous referees for valuable comments. A. M. would like to thank Martin Milanič and Arne Leitert for useful discussions.  ... 
doi:10.1016/j.tcs.2020.01.007 fatcat:jr7cacl2hrc6vbvwbvem2ptike

Semitotal Domination: New hardness results and a polynomial-time algorithm for graphs of bounded mim-width [article]

Esther Galby, Andrea Munaro, Bernard Ries
2018 arXiv   pre-print
In particular, we show that it is solvable in polynomial time for the class of graphs with bounded mim-width by a reduction to Total Dominating Set and we provide several approximation lower bounds for  ...  A semitotal dominating set of a graph G with no isolated vertex is a dominating set D of G such that every vertex in D is within distance two of another vertex in D.  ...  In view of Lemma 9, in order to provide a polynomial-time algorithm for SEMITOTAL DOMINATING SET restricted to dually chordal graphs, it would then be enough to apply a polynomial-time algorithm for TOTAL  ... 
arXiv:1810.06872v1 fatcat:ish56ahevbhilo6n7uupqzxweu

The semitotal domination problem in block graphs

Michael .A. Henning, Saikat Pal, D. Pradhan
2019 Discussiones Mathematicae Graph Theory  
In this paper, we present a linear time algorithm to compute a minimum semitotal dominating set in block graphs.  ...  The semitotal domination problem is known to be NP-complete for chordal graphs and bipartite graphs as shown in [M.A. Henning and A.  ...  In this paper, we design in Section 3 a linear time algorithm for computing a minimum semitotal dominating set in block graphs, a superclass of trees.  ... 
doi:10.7151/dmgt.2254 fatcat:rjubtyg57zacpltjluedjoam3u

Page 4782 of Mathematical Reviews Vol. , Issue 98H [page]

1998 Mathematical Reviews  
As an application we get a linear time approximation of the diameter for weak bipolarizable graphs, a subclass of HHD-free graphs containing all chordal graphs, and an algorithm which computes the diameter  ...  and a diametral pair of vertices of a distance-hereditary graph in linear time.”  ... 

Bounding the Mim-Width of Hereditary Graph Classes [article]

Nick Brettell, Jake Horsfield, Andrea Munaro, Giacomo Paesani, Daniel Paulusma
2020 arXiv   pre-print
A large number of NP-hard graph problems become polynomial-time solvable on graph classes where the mim-width is bounded and quickly computable.  ...  For a given graph H, the class of H-free graphs has bounded mim-width if and only if it has bounded clique-width. We show that the same is not true for (H_1,H_2)-free graphs.  ...  Galby, Munaro and Ries [26] proved that Semitotal Dominating Set is polynomial-time solvable for graph classes where mim-width is bounded and quickly computable.  ... 
arXiv:2004.05018v3 fatcat:327nsviufjgm7pu6iyudggiave

Reducing the Vertex Cover Number via Edge Contractions [article]

Paloma T. Lima, Vinicius F. dos Santos, Ignasi Sau, Uéverton S. Souza, Prafullkumar Tale
2022 arXiv   pre-print
Moreover, unless the ETH fails, the problem does not admit an algorithm running in time f(k + d) · n^o(k + d) for any function f. In particular, this answers the open question stated in Lima et al.  ...  CONTRACTION(vc) can be solved in time 2^O(d)· n^k - d + O(1). This XP algorithm improves the one of Lima et al.  ...  domination number [20] , and the semitotal domination number [18] .  ... 
arXiv:2202.03322v1 fatcat:6w2aszcbzrf6hbvo3avpwzjmpe