Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Trees and co-trees with constant maximum degree in planar 3-connected
  graphs   This paper considers the conjecture by Gr\"unbaum that every planar
3-connected graph has a spanning tree $T$ such that both $T$ and its co-tree
have maximum degree at most 3. Here, the co-tree of $T$ is the spanning tree of
the dual obtained by taking the duals of the non-tree edges. While Gr\"unbaum's
conjecture remains open, we show that every planar 3-connected graph has a
spanning tree $T$ such that both $T$ and its co-tree have maximum degree at
most 5. It can be found in linear time.

25
The categories of this paper are: patt-sol
35
The categories of this paper are: mtrl-th
23
The categories of this paper are: solv-int
36
The categories of this paper are: cmp-lg
30
The categories of this paper are: q-alg
33
The categories of this paper are: plasm-ph
24
The categories of this paper are: dg-ga
4
The categories of this paper are: cond-mat
17
The categories of this paper are: q-fin
7
The categories of this paper are: hep-th
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The categories of this paper are: eess
13
The categories of this paper are: quant-ph
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The categories of this paper are: funct-an
16
The categories of this paper are: stat
26
The categories of this paper are: bayes-an
32
The categories of this paper are: atom-ph