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End spaces and tree-decompositions.
- Source :
-
Journal of Combinatorial Theory - Series B . Jul2023, Vol. 161, p147-179. 33p. - Publication Year :
- 2023
-
Abstract
- We present a systematic investigation into how tree-decompositions of finite adhesion capture topological properties of the space formed by a graph together with its ends. As main results, we characterise when the ends of a graph can be distinguished, and characterise which subsets of ends can be displayed by a tree-decomposition of finite adhesion. In particular, we show that a subset Ψ of the ends of a graph G can be displayed by a tree-decomposition of finite adhesion if and only if Ψ is G δ (a countable intersection of open sets) in | G | , the topological space formed by a graph together with its ends. Since the undominated ends of a graph are easily seen to be G δ , this provides a structural explanation for Carmesin's result that the set of undominated ends can always be displayed. [ABSTRACT FROM AUTHOR]
- Subjects :
- *TOPOLOGICAL spaces
*TOPOLOGICAL property
*INTERSECTION graph theory
*TREE graphs
Subjects
Details
- Language :
- English
- ISSN :
- 00958956
- Volume :
- 161
- Database :
- Academic Search Index
- Journal :
- Journal of Combinatorial Theory - Series B
- Publication Type :
- Academic Journal
- Accession number :
- 163308529
- Full Text :
- https://doi.org/10.1016/j.jctb.2023.02.007