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arXiv · 2404.05026

On two-coloring bipartite uniform hypergraphs

Boyoon Lee·Theodore Molla·Brendan Nagle
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Abstract

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.

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Boyoon Lee, Theodore Molla, Brendan Nagle. 2025-05-14. On two-coloring bipartite uniform hypergraphs. https://arxiv.org/abs/2404.05026

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