Sciweavers

JCT
2006

There are uncountably many topological types of locally finite trees

13 years 11 months ago
There are uncountably many topological types of locally finite trees
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. Key words: graph, locally finite tree, embedding, wqo, bqo Let the tree-order on the set of vertices of a rooted tree T be defined by setting x y for vertices x, y iff x lies on the unique path in T from its root to y. Let us call two locally finite rooted trees equivalent if each of them is a topological minor of the other, with an embedding that respects the treeorder. Call the equivalence classes topological types of such trees. The purpose of this note is to answer a question raised by van der Holst [2], by proving that there are uncountably many topological types of locally finite trees. Our proof uses Nash-Williams's theorem that the
Lilian Matthiesen
Added 13 Dec 2010
Updated 13 Dec 2010
Type Journal
Year 2006
Where JCT
Authors Lilian Matthiesen
Comments (0)