Polynomial-time algorithm for vertex-edge domination number on bounded-treewidth graphs, plus O(c^{sqrt(k)} n) algorithm for k-ve-domination on planar graphs via a treewidth bound of O(sqrt(k)).
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Algorithm for finding vertex-edge domination number on graphs with bounded treewidth and related problems on planar graphs
Polynomial-time algorithm for vertex-edge domination number on bounded-treewidth graphs, plus O(c^{sqrt(k)} n) algorithm for k-ve-domination on planar graphs via a treewidth bound of O(sqrt(k)).