Parameterized Lower Bound and Improved Kernel for Diamond-free Edge Deletion
نویسندگان
چکیده
A diamond is a graph obtained by removing an edge from a complete graph on four vertices. A graph is diamond-free if it does not contain an induced diamond. The Diamond-free Edge Deletion problem asks to find whether there exist at most k edges in the input graph whose deletion results in a diamond-free graph. The problem was proved to be NP-complete and a polynomial kernel of O(k4) vertices was found by Fellows et. al. (Discrete Optimization, 2011). In this paper, we give an improved kernel of O(k3) vertices for Diamond-free Edge Deletion. We give an alternative proof of the NP-completeness of the problem and observe that it cannot be solved in time 2o(k) · nO(1), unless Exponential Time Hypothesis fails. 1998 ACM Subject Classification F.2.2. Nonnumerical Algorithms and Problems
منابع مشابه
Improved Kernels and Algorithms for Claw and Diamond Free Edge Deletion Based on Refined Observations
In the {Claw, Diamond}-Free Edge Deletion problem, we are given a graph G and an integer k > 0, the question is whether there are at most k edges whose deletion results in a graph without claws and diamonds as induced graphs. Based on some refined observations, we propose a kernel of O(k3) vertices and O(k4) edges, significantly improving the previous kernel of O(k12) vertices and O(k24) edges....
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