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The paper doi:10.7151/dmgt.1639On Properties of Maximal 1-planar Graphs by Dávid Hudák, Tomáš Madaras and Yusuke Suzuki describes the construction of maximal 1-planar graphs with minimum degree 2 and with (relatively) small number of edges, namely, (8/3)*(n-2) (which is far less than the number of edges of a maximal n-vertex planar graph).

The paper doi:10.7151/dmgt.1639 describes the construction of maximal 1-planar graphs with minimum degree 2 and with (relatively) small number of edges, namely, (8/3)*(n-2) (which is far less than the number of edges of a maximal n-vertex planar graph).

The paper On Properties of Maximal 1-planar Graphs by Dávid Hudák, Tomáš Madaras and Yusuke Suzuki describes the construction of maximal 1-planar graphs with minimum degree 2 and with (relatively) small number of edges, namely, (8/3)*(n-2) (which is far less than the number of edges of a maximal n-vertex planar graph).

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The paper doi:10.7151/dmgt.1639 describes the construction of maximal 1-planar graphs with minimum degree 2 and with (relatively) small number of edges, namely, (8/3)*(n-2) (which is far less than the number of edges of a maximal n-vertex planar graph).