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