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arXiv · 2304.11691

Covering multigraphs with bipartite graphs

Jaehoon Kim·Hyunwoo Lee
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Abstract

Hansel's lemma states that $\sum_{H\in \mathcal{H}}|H| \geq n \log_2 n$ holds where $\mathcal{H}$ is a collection of bipartite graphs covering all the edges of $K_n$. We generalize this lemma to the corresponding multigraph covering problem and the graphon covering problem. We also prove an upper bound on $\sum_{H\in \mathcal{H}}|H|$ which shows that our generalization is asymptotically tight in some sense.

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Jaehoon Kim, Hyunwoo Lee. 2023-04-23. Covering multigraphs with bipartite graphs. https://arxiv.org/abs/2304.11691

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