All graphs have tree-decompositions displaying their topological ends

2014/09/23 by Carmesin, Johannes · 1 citation
#05B35 #05C63 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.1409.6640

Abstract

We show that every connected graph has a spanning tree that displays all its topological ends. This proves a 1964 conjecture of Halin in corrected form, and settles a problem of Diestel from 1992.

Cited by

• Topological cycle matroids of infinite graphs

Related

• Constructing tree-decompositions that display all topological ends
• End spaces and tree-decompositions
• Progress on sufficient conditions for a graph to have a spanning k-ended tree
• End-faithful spanning trees in graphs without normal spanning trees
• A representation theorem for end spaces of infinite graphs