Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Axis-Aligned Square Contact Representations   We introduce a new class $\mathcal{G}$ of bipartite plane graphs and prove
that each graph in $\mathcal{G}$ admits a proper square contact representation.
A contact between two squares is \emph{proper} if they intersect in a line
segment of positive length. The class $\mathcal{G}$ is the family of
quadrangulations obtained from the 4-cycle $C_4$ by successively inserting a
single vertex or a 4-cycle of vertices into a face.
  For every graph $G\in \mathcal{G}$, we construct a proper square contact
representation. The key parameter of the recursive construction is the aspect
ratio of the rectangle bounded by the four outer squares. We show that this
aspect ratio may continuously vary in an interval $I_G$. The interval $I_G$
cannot be replaced by a fixed aspect ratio, however, as we show, the feasible
interval $I_G$ may be an arbitrarily small neighborhood of any positive real.

23
The categories of this paper are: solv-int
28
The categories of this paper are: alg-geom
15
The categories of this paper are: nucl-ex
22
The categories of this paper are: chao-dyn
35
The categories of this paper are: mtrl-th
19
The categories of this paper are: eess
16
The categories of this paper are: stat
18
The categories of this paper are: econ
37
The categories of this paper are: supr-con
33
The categories of this paper are: plasm-ph
12
The categories of this paper are: nucl-th
31
The categories of this paper are: ao-sci
7
The categories of this paper are: hep-th
14
The categories of this paper are: math-ph
26
The categories of this paper are: bayes-an
21
The categories of this paper are: adap-org