Emergent Mind
Improved Kernels and Algorithms for Claw and Diamond Free Edge Deletion Based on Refined Observations
(1707.06779)
Published Jul 21, 2017
in
cs.DS
Abstract
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 $O(k{12})$ vertices and $O(k{24})$ edges. In addition, we derive an $O*(3.792k)$-time algorithm for the {claw, diamond}-free edge deletion problem.
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