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

Peng Li () and Aifa Wang ()
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Peng Li: Chongqing University of Technology
Aifa Wang: Chongqing University of Technology

Journal of Combinatorial Optimization, 2023, vol. 45, issue 1, No 52, 16 pages

Abstract: 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 $$O(k|S|+m)$$ 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.

Keywords: Vertex-edge domination; Double vertex-edge domination; k-vertex-edge domination; Polynomial time algorithm; Interval graphs (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s10878-022-00982-8

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