Kriesell's conjecture for infinite graphs
Abstract
Let G be a graph and S⊆ V(G) be a subset of vertices. An S-Steiner tree T of G is a tree of G which contains S in its vertex set V(T). Kriesell conjectured that for every 2k-edge-connected subset S⊆ V(G) in a finite connected graph G, there exist k pairwise edge-disjoint S-Steiner trees. This conjecture is false for infinite graphs. We present a version of Kriesell's conjecture with topological S-Steiner trees for countable finitely edge-separable graphs and a version with F-limits of trees for rayless graphs. We show that if Kriesell's conjecture holds for finite graphs, then it holds for every connected, rayless and finitely edge-separable graph. We also show that every 2k-edge-connected rayless and finitely edge-separable graph contains k pairwise edge-disjoint spanning trees.
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BibTeX
@misc{aurichi2026kriesells,
title = {{Kriesell's conjecture for infinite graphs}},
author = {Leandro Aurichi and Paulo Magalhães Júnior and Rodrigo Santos Monteiro},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.11534},
eprint = {2609.11534},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.11534},
}
RIS
TY - UNPB
TI - Kriesell's conjecture for infinite graphs
AU - Leandro Aurichi
AU - Paulo Magalhães Júnior
AU - Rodrigo Santos Monteiro
PY - 2026
DA - 2026/09/10
PB - arXiv
DO - 10.48550/arxiv.2609.11534
UR - https://arxiv.org/abs/2609.11534
AB - Let G be a graph and S⊆ V(G) be a subset of vertices. An S-Steiner tree T of G is a tree of G which contains S in its vertex set V(T). Kriesell conjectured that for every 2k-edge-connected subset S⊆ V(G) in a finite connected graph G, there exist k pairwise edge-disjoint S-Steiner trees. This conjecture is false for infinite graphs. We present a version of Kriesell's conjecture with topological S-Steiner trees for countable finitely edge-separable graphs and a version with F-limits of trees for rayless graphs. We show that if Kriesell's conjecture holds for finite graphs, then it holds for every connected, rayless and finitely edge-separable graph. We also show that every 2k-edge-connected rayless and finitely edge-separable graph contains k pairwise edge-disjoint spanning trees.
ER -