Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Immersions in highly edge connected graphs   We consider the problem of how much edge connectivity is necessary to force a
graph G to contain a fixed graph H as an immersion. We show that if the maximum
degree in H is D, then all the examples of D-edge connected graphs which do not
contain H as a weak immersion must have a tree-like decomposition called a
tree-cut decomposition of bounded width. If we consider strong immersions, then
it is easy to see that there are arbitrarily highly edge connected graphs which
do not contain a fixed clique K_t as a strong immersion. We give a structure
theorem which roughly characterizes those highly edge connected graphs which do
not contain K_t as a strong immersion.

36
The categories of this paper are: cmp-lg
34
The categories of this paper are: chem-ph
4
The categories of this paper are: cond-mat
15
The categories of this paper are: nucl-ex
28
The categories of this paper are: alg-geom
1
The categories of this paper are: cs
37
The categories of this paper are: supr-con
35
The categories of this paper are: mtrl-th
30
The categories of this paper are: q-alg
3
The categories of this paper are: physics
5
The categories of this paper are: gr-qc
23
The categories of this paper are: solv-int
22
The categories of this paper are: chao-dyn
10
The categories of this paper are: q-bio
32
The categories of this paper are: atom-ph
17
The categories of this paper are: q-fin