Matthiesen, Lilian There are uncountably many topological types of locally finite trees. (English) Zbl 1094.05019 J. Comb. Theory, Ser. B 96, No. 5, 758-760 (2006). Summary: Consider two locally finite rooted trees as equivalent if each of them is a topological minor of the other, with an embedding preserving the tree-order. Answering a question of van der Holst, we prove that there are uncountably many equivalence classes. Cited in 2 ReviewsCited in 5 Documents MSC: 05C05 Trees 05C10 Planar graphs; geometric and topological aspects of graph theory Keywords:graph; locally finite tree; embedding PDFBibTeX XMLCite \textit{L. Matthiesen}, J. Comb. Theory, Ser. B 96, No. 5, 758--760 (2006; Zbl 1094.05019) Full Text: DOI References: [1] Diestel, R., Graph Theory (2005), Springer-Verlag: Springer-Verlag New York · Zbl 1074.05001 [2] H. van der Holst, Problem posed at the 2005 Graph Theory workshop at Oberwolfach; H. van der Holst, Problem posed at the 2005 Graph Theory workshop at Oberwolfach [3] Kühn, D., On well-quasi-ordering infinite trees—Nash-Williams’s theorem revisited, Math. Proc. Cambridge Philos. Soc., 130, 401-408 (2001) · Zbl 0985.05017 [4] Nash-Williams, C. St. J.A., On well-quasi-ordering infinite trees, Proc. Cambridge Philos. Soc., 61, 697-720 (1965) · Zbl 0144.23305 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.