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arXiv · 2111.12670

A representation theorem for end spaces of infinite graphs

Jan Kurkofka·Max Pitz
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Abstract

End-spaces of infinite graphs naturally generalise the Freudenthal boundary and sit at the interface between graph theory, geometric group theory and topology. Our main result is that every end-space can topologically be represented by a special order tree. Our main proof ingredient is a structure theorem that we introduce, which carves out the order-tree-like structure of any graph in such a way that there is a natural bijection between the ends of the graph and the limit-type down-closed chains of the order-tree.

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Jan Kurkofka, Max Pitz. 2024-08-30. A representation theorem for end spaces of infinite graphs. https://arxiv.org/abs/2111.12670

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