## Abstract

End spaces of infinite graphs sit at the interface between graph theory, group theory and topology. They arise as the boundary of an infinite graph in a standard sense generalising the theory of the Freudenthal boundary developed by Freudenthal and Hopf in the 1940's for infinite groups.

A long-standing quest in infinite graph theory with a rich body of literature seeks to describe the possible end structures of graphs by a set of low-complexity representatives. In this paper we propose a solution to this fifty-year-old problem by showing that every end space is homeomorphic to the end space of some (uniform graph on a) special order tree.

A long-standing quest in infinite graph theory with a rich body of literature seeks to describe the possible end structures of graphs by a set of low-complexity representatives. In this paper we propose a solution to this fifty-year-old problem by showing that every end space is homeomorphic to the end space of some (uniform graph on a) special order tree.

Original language | English |
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Publisher | arXiv |

DOIs | |

Publication status | Published - 2 Mar 2023 |