Complexity of Paired Domination in AT-free and Planar Graphs

Vikash Tripathi, Ton Kloks, Arti Pandey*, Kaustav Paul, Hung Lung Wang


研究成果: 書貢獻/報告類型會議論文篇章


For a graph G= (V, E), a subset D of vertex set V, is a dominating set of G if every vertex not in D is adjacent to atleast one vertex of D. A dominating set D of a graph G with no isolated vertices is called a paired dominating set (PD-set), if G[D], the subgraph induced by D in G has a perfect matching. The Min-PD problem requires to compute a PD-set of minimum cardinality. The decision version of the Min-PD problem remains NP-complete even when G belongs to restricted graph classes such as bipartite graphs, chordal graphs etc. On the positive side, the problem is efficiently solvable for many graph classes including intervals graphs, strongly chordal graphs, permutation graphs etc. In this paper, we study the complexity of the problem in AT-free graphs and planar graph. The class of AT-free graphs contains cocomparability graphs, permutation graphs, trapezoid graphs, and interval graphs as subclasses. We propose a polynomial-time algorithm to compute a minimum PD-set in AT-free graphs. In addition, we also present a linear-time 2-approximation algorithm for the problem in AT-free graphs. Further, we prove that the decision version of the problem is NP-complete for planar graphs, which answers an open question asked by Lin et al. (in Theor. Comput. Sci., 591 (2015 ) : 99 - 105 and Algorithmica, 82 (2020 ) : 2809 - 2840 ).

主出版物標題Algorithms and Discrete Applied Mathematics - 8th International Conference, CALDAM 2022, Proceedings
編輯Niranjan Balachandran, R. Inkulu
發行者Springer Science and Business Media Deutschland GmbH
出版狀態已發佈 - 2022
事件8th International Conference on Algorithms and Discrete Applied Mathematics, CALDAM 2022 - Puducherry, 印度
持續時間: 2022 2月 102022 2月 12


名字Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
13179 LNCS


會議8th International Conference on Algorithms and Discrete Applied Mathematics, CALDAM 2022

ASJC Scopus subject areas

  • 理論電腦科學
  • 電腦科學(全部)


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