Parameterized Complexity of Upper Edge Domination

08/04/2022

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by   Ajinkya Gaikwad, et al.

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In this paper we study a maximization version of the classical Edge Dominating Set (EDS) problem, namely, the Upper EDS problem, in the realm of Parameterized Complexity. In this problem, given an undirected graph G, a positive integer k, the question is to check whether G has a minimal edge dominating set of size at least k. We obtain the following results for Upper EDS. We prove that Upper EDS admits a kernel with at most 4k^2-2 vertices. We also design a fixed-parameter tractable (FPT) algorithm for Upper EDS running in time 2^𝒪(k)· n^𝒪(1).