### arXiv:2101.05264 [math.CO]AbstractReferencesReviewsResources

#### Hamiltonicity in infinite tournaments

Published 2021-01-13Version 1

We prove that for all countable tournaments $D$ the recently discovered compactification $|D|$ by their ends and limit edges contains a topological Hamilton path: a topological arc that contains every vertex. If $D$ is strongly connected, then $|D|$ contains a topological Hamilton circle. These results extend well-known theorems about finite tournaments, which we show do not extend to the infinite in a purely combinatorial setting.

**Comments:**13 pages, 4 figures

**Categories:**math.CO

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