A Polynomial Kernel for Proper Helly Circular-arc Vertex Deletion
Abstract
A proper Helly circular-arc graph is an intersection graph of a set of arcs on a circle such that none of the arcs properly contains any other arc and every set of pairwise intersecting arcs has a common intersection. The Proper Helly Circular-arc Vertex Deletion problem takes as input a graph $G$ and an integer $k$, and the goal is to check if we can remove at most $k$ vertices from the graph to obtain a proper Helly circular-arc graph; the parameter is $k$. Recently, Cao et al.~[MFCS 2023] obtained an FPT algorithm for this (and related) problem. In this work, we obtain a polynomial kernel for the problem.
- Publication:
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arXiv e-prints
- Pub Date:
- January 2024
- DOI:
- 10.48550/arXiv.2401.03415
- arXiv:
- arXiv:2401.03415
- Bibcode:
- 2024arXiv240103415A
- Keywords:
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- Computer Science - Discrete Mathematics;
- Mathematics - Combinatorics
- E-Print:
- 25 pages, 3 figures, In LATIN 2024