A locally finite tree that behaves like an infinite star

TL;DR

This paper constructs a special infinite tree with degree 3 that remains structurally unchanged when finitely many leaves are removed, mimicking an infinite star's properties.

Contribution

It introduces a novel infinite tree structure that is resilient to finite leaf removals, demonstrating a unique form of local finiteness and self-similarity.

Findings

Tree T has maximal degree 3 and infinitely many leaves.

Removing finitely many leaves leaves the tree isomorphic to itself.

Tree T behaves like an infinite star in terms of structural invariance.

Abstract

We construct a tree T of maximal degree 3 with infinitely many leaves such that whenever finitely many of them are removed, the remaining tree is isomorphic to T. In this sense T resembles an infinite star.