Straight-Line Grid Drawings of 3-Connected 1-Planar Graphs

descriptionPublicationkeyboard_double_arrow_right Part of book or chapter of book , Conference object , Article 01 Jan 2013Publisher:Springer International Publishing

Authors: Md. Jawaherul Alam; Franz J. Brandenburg; Stephen G. Kobourov;

doi: 10.1007/978-3-319-03841-4_8

Straight-Line Grid Drawings of 3-Connected 1-Planar Graphs

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Abstract

A graph is 1-planar if it can be drawn in the plane such that each edge is crossed at most once. In general, 1-planar graphs do not admit straight-line drawings. We show that every 3-connected 1-planar graph has a straight-line drawing on an integer grid of quadratic size, with the exception of a single edge on the outer face that has one bend. The drawing can be computed in linear time from any given 1-planar embedding of the graph.

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