On topological and combinatorial properties of edge-ends

• Grant number: 25/00669-5
• Support Opportunities: Scholarships abroad - Research Internship - Doctorate
• Start date: October 06, 2025
• End date: October 05, 2026
• Field of knowledge: Physical Sciences and Mathematics - Mathematics
• Principal Investigator: Leandro Fiorini Aurichi
• Grantee: Lucas Silva Sinzato Real
• Supervisor: Max Pitz
• Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil
• Institution abroad: Universität Hamburg (UHH), Germany
• Associated to the scholarship: 24/01158-1 - Directions in Infinite Graphs: topological, combinatorial and set-theoretical approaches, BP.DR

Abstract

The combinatorial and topological properties of end spaces have been explored by an extensive bibliography within infinite graph theory. On the other hand, the edge-related counterpart to these structures does not benefit from such a well established literature. In fact, besides a first article due to Hahn, Laviolette and Sirán, almost no other reference brings a deeper investigation about edge-ends of infinite graphs. In a recent work partially supported by FAPESP, however, the student and his supervisor in Brazil coauthored a paper which highlights that these latter objects indeed behave differently from the broadly studied end spaces. Then, this internship research proposal aims to reach a more complete picture of the edge-end structure in infinite graphs. In our approach, this goal shall be addressed especially by revisiting some landmark theorems in the classical end space theory and searching for their edge-analogous conclusions.