Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Hadwiger and Helly-type theorems for disjoint unit spheres   We prove Helly-type theorems for line transversals to disjoint unit balls in
$\R^{d}$. In particular, we show that a family of $n \geq 2d$ disjoint unit
balls in $\R^d$ has a line transversal if, for some ordering $\prec$ of the
balls, any subfamily of 2d balls admits a line transversal consistent with
$\prec$. We also prove that a family of $n \geq 4d-1$ disjoint unit balls in
$\R^d$ admits a line transversal if any subfamily of size $4d-1$ admits a
transversal.

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The categories of this paper are: hep-ph
15
The categories of this paper are: nucl-ex
32
The categories of this paper are: atom-ph
12
The categories of this paper are: nucl-th
9
The categories of this paper are: nlin
29
The categories of this paper are: funct-an
30
The categories of this paper are: q-alg
33
The categories of this paper are: plasm-ph
16
The categories of this paper are: stat
21
The categories of this paper are: adap-org
26
The categories of this paper are: bayes-an
27
The categories of this paper are: comp-gas
11
The categories of this paper are: hep-lat
37
The categories of this paper are: supr-con
36
The categories of this paper are: cmp-lg
23
The categories of this paper are: solv-int