Improved parameterized algorithms and kernels for mixed domination

摘要

A mixed domination of a graph G =(V, E) is a mixed set Dof vertices and edges such that for every edge or vertex, if it is not in D, then it is adjacent or incident to at least one vertex or edge in D. TheMixed Dominationproblem is to check whether there is a mixed domination of size at most kin a graph. Mixed domination is a mixture concept of vertex domination and edge domination, and the mixed domination problem has been studied from the view of approximation algorithms, parameterized algorithms, and so on. In this paper, we give a branch-and-search algorithm with running time bound of O*(4.172k), which improves the previous bound of O* (7.465k). For kernelization, it is known that the problem parameterized by kin general graphs is unlikely to have a polynomial kernel. We show the problem in planar graphs allows linear kernel by giving a kernel of 11k - 16 vertices. (C) 2020 Elsevier B.V. All rights reserved.