Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Extremal results regarding $K_6$-minors in graphs of girth at least 5   We prove that every 6-connected graph of girth $\geq 6$ has a $K_6$-minor and
thus settle the Jorgensen conjecture for graphs of girth $ \geq 6$. Relaxing
the assumption on the girth, we prove that every 6-connected $n$-vertex graph
of size $\geq 3 1/5 n-8$ and of girth $\geq 5$ contains a $K_6$-minor.

19
The categories of this paper are: eess
15
The categories of this paper are: nucl-ex
26
The categories of this paper are: bayes-an
21
The categories of this paper are: adap-org
22
The categories of this paper are: chao-dyn
11
The categories of this paper are: hep-lat
33
The categories of this paper are: plasm-ph
23
The categories of this paper are: solv-int
27
The categories of this paper are: comp-gas
16
The categories of this paper are: stat
28
The categories of this paper are: alg-geom
1
The categories of this paper are: cs
12
The categories of this paper are: nucl-th
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The categories of this paper are: dg-ga
29
The categories of this paper are: funct-an
31
The categories of this paper are: ao-sci