On two-coloring bipartite uniform hypergraphs
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866909609767206912 |
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| author | Lee, Boyoon Molla, Theodore Nagle, Brendan |
| author_facet | Lee, Boyoon Molla, Theodore Nagle, Brendan |
| contents | Of a given bipartite graph $G = (V, E)$, it is elementary to construct a bipartition in time $O(|V| + |E|)$. For a given $k$-graph $H = H^{(k)}$ with $k \geq 3$ fixed, Lovász proved that deciding whether $H$ is bipartite is NP-complete. Let $\mathcal{B}_n$ denote the collection of all $[n]$-vertex bipartite $k$-graphs. We construct, of a given $H \in \mathcal{B}_n$, a bipartition in time averaging $O(n^k)$ over the class $\mathcal{B}_n$. We provide two proofs of our result. When $k = 3$, this result expedites one of Person and Schacht. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_05026 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On two-coloring bipartite uniform hypergraphs Lee, Boyoon Molla, Theodore Nagle, Brendan Combinatorics Of a given bipartite graph $G = (V, E)$, it is elementary to construct a bipartition in time $O(|V| + |E|)$. For a given $k$-graph $H = H^{(k)}$ with $k \geq 3$ fixed, Lovász proved that deciding whether $H$ is bipartite is NP-complete. Let $\mathcal{B}_n$ denote the collection of all $[n]$-vertex bipartite $k$-graphs. We construct, of a given $H \in \mathcal{B}_n$, a bipartition in time averaging $O(n^k)$ over the class $\mathcal{B}_n$. We provide two proofs of our result. When $k = 3$, this result expedites one of Person and Schacht. |
| title | On two-coloring bipartite uniform hypergraphs |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2404.05026 |