Semilinear and terrain-like graphs on n vertices have biclique covers of size O(n polylog n), while some unit disk graphs require Ω(n^{4/3}) size.
Ramsey properties of semilinear graphs
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Compact Representation of Semilinear and Terrain-like Graphs
Semilinear and terrain-like graphs on n vertices have biclique covers of size O(n polylog n), while some unit disk graphs require Ω(n^{4/3}) size.