Volltext
Abstract: Initial steps in the study of inner expansion properties of in finite Cay- ley graphs and other in finite graphs, such as hyperbolic ones, are taken, in a flavor similar to the well-known Lipton-Tarjan √
n separation result for planar graphs.
Connections to relaxed versions of quasi-isometries are explored, such as regular and semiregular maps. This is joint work with I. Benjamini and O. Schramm.
1
ÄHNLICHE DOKUMENTE
[11] There is no locally finite 2-connected infinite graph in which the topological cycle space has a simple generating set in the vector space sense (i.e. allowing only finite
But in general, normal trees T ⊆ G containing U all whose rays are dominated in G are not complementary to undominated combs, because the absence of an undominated comb does not
In Section 2.3 we use similar techniques to extend the cycle double cover conjecture and Seymour’s faithful cycle cover conjecture to locally finite graphs: if these conjectures
The key in an infinite setting is that dual trees must share between them not only the edges of their host graphs but also their ends: the statement that a set of edges is acyclic
Note that for graphs with bounded maximal degree the definition of accessibility is equivalent to the following: A graph of bounded maximal degree is accessible if and only if
In Chapter 6 we will then define our new homology theory for locally compact spaces and show that it satisfies the axioms for homology and coincides with the topological cycle space
In fact, if we consider graphs with a bounded maximum degree, then a larger number of edges is allowed... We also remark that such a conjecture is related to the
As mentioned in the introduction, in order to extend Theorem 4.2 to locally finite infinite graphs, we would like to prove that for any 2-connected locally finite infinite graph G,
