Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Book Thickness of 1-Planar Graphs   In a book embedding of a graph G, the vertices of G are placed in order along
a straight-line called spine of the book, and the edges of G are drawn on a set
of half-planes, called the pages of the book, such that two edges drawn on a
page do not cross each other. The minimum number of pages in which a graph can
be embedded is called the book-thickness or the page-number of the graph. It is
known that every planar graph has a book embedding on at most four pages. Here
we investigate the book-embeddings of 1-planar graphs. A graph is 1-planar if
it can be drawn in the plane such that each edge is crossed at most once. We
prove that every 1-planar graph has a book embedding on at most 16 pages and
every 3-connected 1-planar graph has a book embedding on at most 12 pages. The
drawings can be computed in linear time from any given 1-planar embedding of
the graph.

18
The categories of this paper are: econ
14
The categories of this paper are: math-ph
5
The categories of this paper are: gr-qc
6
The categories of this paper are: astro-ph
23
The categories of this paper are: solv-int
25
The categories of this paper are: patt-sol
22
The categories of this paper are: chao-dyn
12
The categories of this paper are: nucl-th
17
The categories of this paper are: q-fin
13
The categories of this paper are: quant-ph
31
The categories of this paper are: ao-sci
37
The categories of this paper are: supr-con
2
The categories of this paper are: math
34
The categories of this paper are: chem-ph
21
The categories of this paper are: adap-org
35
The categories of this paper are: mtrl-th