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arXiv · 1707.04917

Feedback Vertex Set Inspired Kernel for Chordal Vertex Deletion

Akanksha Agrawal·Daniel Lokshtanov·Pranabendu Misra·Saket Saurabh·Meirav Zehavi
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Abstract

Given a graph $G$ and a parameter $k$, the Chordal Vertex Deletion (CVD) problem asks whether there exists a subset $U\subseteq V(G)$ of size at most $k$ that hits all induced cycles of size at least 4. The existence of a polynomial kernel for CVD was a well-known open problem in the field of Parameterized Complexity. Recently, Jansen and Pilipczuk resolved this question affirmatively by designing a polynomial kernel for CVD of size $O(k^{161}\log^{58}k)$, and asked whether one can design a kernel of size $O(k^{10})$. While we do not completely resolve this question, we design a significantly smaller kernel of size $O(k^{12}\log^{10}k)$, inspired by the $O(k^2)$-size kernel for Feedback Vertex Set. Furthermore, we introduce the notion of the independence degree of a vertex, which is our main conceptual contribution.

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Akanksha Agrawal, Daniel Lokshtanov, Pranabendu Misra, Saket Saurabh, Meirav Zehavi. 2017-07-16. Feedback Vertex Set Inspired Kernel for Chordal Vertex Deletion. https://arxiv.org/abs/1707.04917

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