## January 20, 2017:

#
Square Dissections and Square Contact Representations

##
Will Devanny

A square contact representation is a representation of a graph where
interior disjoint squares are used to represent vertices and edges of
the graph correspond to side-side contacts between pairs of squares. One
way to define a square dissection is as a square contact representation
where the union of the squares forms a rectangle. It is an open question
whether or not bipartite planar graphs admit square contact
representations. We will present a selection of results on square
dissections and square contact representations from “Rectangle and
Square Representations of Planar Graphs”, a survey by Felsner, along with
a couple of modest steps by Alam, Da Lozzo, D., and Johnson towards
classifying which graphs admit square contact representations.