We introduce a new class G of plane bipartite graphs and prove that each graph in G admits a proper square contact representation. A contact between two squares is proper if they intersect in a line segment of positive length. The class 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  .
We introduce a new class G of bipartite plane graphs and prove that each graph in G admits a proper square contact representation. A contact between two squares is proper if they intersect in a line segment of positive length. The class 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 .
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plane bipartite
bipartite plane
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. For every graph G\in \mathcal{G