# Infinite end-devouring sets of rays with prescribed start vertices

## TL;DR

This paper proves a significant property of graph ends, showing they contain either uncountably many disjoint rays or a universal set of rays starting at any chosen vertices, confirming a conjecture.

## Contribution

It establishes a new fundamental result about the structure of graph ends, confirming Georgakopoulos's conjecture.

## Key findings

- Ends contain uncountably many disjoint rays or a universal set meeting all rays.
- Confirms a longstanding conjecture in graph theory.
- Provides a new understanding of the structure of rays in graph ends.

## Abstract

We prove that every end of a graph contains either uncountably many disjoint rays or a set of disjoint rays that meet all rays of the end and start at any prescribed feasible set of start vertices. This confirms a conjecture of Georgakopoulos.