Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Gap-planar Graphs   We introduce the family of $k$-gap-planar graphs for $k \geq 0$, i.e., graphs
that have a drawing in which each crossing is assigned to one of the two
involved edges and each edge is assigned at most $k$ of its crossings. This
definition is motivated by applications in edge casing, as a $k$-gap-planar
graph can be drawn crossing-free after introducing at most $k$ local gaps per
edge. We present results on the maximum density of $k$-gap-planar graphs, their
relationship to other classes of beyond-planar graphs, characterization of
$k$-gap-planar complete graphs, and the computational complexity of recognizing
$k$-gap-planar graphs.

11
The categories of this paper are: hep-lat
28
The categories of this paper are: alg-geom
25
The categories of this paper are: patt-sol
27
The categories of this paper are: comp-gas
37
The categories of this paper are: supr-con
19
The categories of this paper are: eess
32
The categories of this paper are: atom-ph
8
The categories of this paper are: hep-ex
30
The categories of this paper are: q-alg
21
The categories of this paper are: adap-org
34
The categories of this paper are: chem-ph
36
The categories of this paper are: cmp-lg
13
The categories of this paper are: quant-ph
6
The categories of this paper are: astro-ph
3
The categories of this paper are: physics
0
The categories of this paper are: hep-ph