Finding hypergraph immersion is fixed-parameter tractable
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866912131838902272 |
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| author | Meng, Xiangyi Tian, Yu |
| author_facet | Meng, Xiangyi Tian, Yu |
| contents | Immersion minor is an important variant of graph minor, defined through an injective mapping from vertices in a smaller graph $H$ to vertices in a larger graph $G$ where adjacent elements of the former are connected in the latter by edge-disjoint paths. Here, we consider the immersion problem in the emerging field of hypergraphs. We first define hypergraph immersion by extending the injective mapping to hypergraphs. We then prove that finding a hypergraph immersion is fixed-parameter tractable, namely, there exists an $O(N^6)$ polynomial-time algorithm to determine whether a fixed hypergraph $H$ can be immersed in a hypergraph $G$ with $N$ vertices. Additionally, we present the dual hypergraph immersion problem and provide further characteristics of the algorithmic complexity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_16017 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Finding hypergraph immersion is fixed-parameter tractable Meng, Xiangyi Tian, Yu Discrete Mathematics Combinatorics 05C83, 05C85, 05C65 Immersion minor is an important variant of graph minor, defined through an injective mapping from vertices in a smaller graph $H$ to vertices in a larger graph $G$ where adjacent elements of the former are connected in the latter by edge-disjoint paths. Here, we consider the immersion problem in the emerging field of hypergraphs. We first define hypergraph immersion by extending the injective mapping to hypergraphs. We then prove that finding a hypergraph immersion is fixed-parameter tractable, namely, there exists an $O(N^6)$ polynomial-time algorithm to determine whether a fixed hypergraph $H$ can be immersed in a hypergraph $G$ with $N$ vertices. Additionally, we present the dual hypergraph immersion problem and provide further characteristics of the algorithmic complexity. |
| title | Finding hypergraph immersion is fixed-parameter tractable |
| topic | Discrete Mathematics Combinatorics 05C83, 05C85, 05C65 |
| url | https://arxiv.org/abs/2411.16017 |