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arXiv · 1711.08185

Minimum co-degree condition for perfect matchings in k-partite k-graphs

Hongliang Lu·Yan Wang·Xingxing Yu
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Abstract

Let $H$ be a $k$-partite $k$-graph with $n$ vertices in each partition class, and let $\delta_{k-1}(H)$ denote the minimum co-degree of $H$. We characterize those $H$ with $\delta_{k-1}(H) \geq n/2$ and with no perfect matching. As a consequence we give an affirmative answer to the following question of R\"odl and Ruci\'nski: If $k$ is even or $n \not\equiv 2 \pmod 4$, does $\delta_{k-1}(H) \geq n/2$ imply that $H$ has a perfect matching? We also give an example indicating that it is not sufficient to impose this degree bound on only two types of $(k-1)$-sets.

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Hongliang Lu, Yan Wang, Xingxing Yu. 2017-11-22. Minimum co-degree condition for perfect matchings in k-partite k-graphs. https://arxiv.org/abs/1711.08185

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