Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: New representation results for planar graphs   A universal representation theorem is derived that shows any graph is the
intersection graph of one chordal graph, a number of co-bipartite graphs, and
one unit interval graph. Central to the the result is the notion of the clique
cover width which is a generalization of the bandwidth parameter. Specifically,
we show that any planar graph is the intersection graph of one chordal graph,
four co-bipartite graphs, and one unit interval graph. Equivalently, any planar
graph is the intersection graph of a chordal graph and a graph that has {clique
cover width} of at most seven. We further describe the extensions of the
results to graphs drawn on surfaces and graphs excluding a minor of crossing
number of at most one.

12
The categories of this paper are: nucl-th
33
The categories of this paper are: plasm-ph
35
The categories of this paper are: mtrl-th
37
The categories of this paper are: supr-con
30
The categories of this paper are: q-alg
6
The categories of this paper are: astro-ph
19
The categories of this paper are: eess
14
The categories of this paper are: math-ph
29
The categories of this paper are: funct-an
20
The categories of this paper are: acc-phys
10
The categories of this paper are: q-bio
16
The categories of this paper are: stat
17
The categories of this paper are: q-fin
15
The categories of this paper are: nucl-ex
8
The categories of this paper are: hep-ex
21
The categories of this paper are: adap-org