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Polynomial time algorithm for k-vertex-edge dominating problem in interval graphs

Journal of Combinatorial Optimization volume 45, Article number: 45 (2023) Cite this article

Abstract

Let G be a connected interval graph with n vertices and m edges. For any positive integer k and any subset S of E(G), we design an \(O(k|S|+m)\) time algorithm to find a minimum k-vertex-edge dominating set of G with respect to S. This shows that the vertex-edge domination problem and the double vertex-edge domination problem can be solved in linear time. Furthermore, the k-vertex-edge domination problem can also be solved in O(km) time algorithm in interval graphs. Finally, we present a linear time algorithm to solve the independent vertex-edge domination problem for unit interval graphs.

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Funding

We thank the referees and editors for their constructive input. This work was supported by the National Natural Science Foundation of China (11701059), the Natural Science Foundation of Chongqing (cstc2020jcyj-msxmX0272, cstc2021jcyj-msxmX0436), the Youth project of science and technology research program of Chongqing Education Commission of China (KJQN202 001130, KJQN202001107, KJQN202101130).

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  1. Chongqing University of Technology, 69 Hongguang Road, Chongqing, China

    Peng Li & Aifa Wang

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  1. Peng Li
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  2. Aifa Wang
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Correspondence to Aifa Wang.

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This is the updated version of a conference paper that was presented at AAIM 2022 (Li and Wang 2022).

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Li, P., Wang, A. Polynomial time algorithm for k-vertex-edge dominating problem in interval graphs. J Comb Optim 45, 45 (2023). https://doi.org/10.1007/s10878-022-00982-8

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  • DOI: https://doi.org/10.1007/s10878-022-00982-8

Keywords

  • Vertex-edge domination
  • Double vertex-edge domination
  • k-vertex-edge domination
  • Polynomial time algorithm
  • Interval graphs