A Polynomial Kernel for Proper Helly Circular-arc Vertex Deletion
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866911750057623552 |
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| author | Agrawal, Akanksha Jana, Satyabrata Sahu, Abhishek |
| author_facet | Agrawal, Akanksha Jana, Satyabrata Sahu, Abhishek |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_03415 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Polynomial Kernel for Proper Helly Circular-arc Vertex Deletion Agrawal, Akanksha Jana, Satyabrata Sahu, Abhishek Discrete Mathematics Combinatorics 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. |
| title | A Polynomial Kernel for Proper Helly Circular-arc Vertex Deletion |
| topic | Discrete Mathematics Combinatorics |
| url | https://arxiv.org/abs/2401.03415 |