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The geometric thickness of a graph is the minimum number of layers such that the graph can be drawn in the plane with edges as straight-line segments, and with each edge assigned to a layer so that no two edges in the same layer cross. We consider a variation on this theme in which each edge is allowed one bend. We prove that the vertices of an n-vertex m-edge graph can be positioned in a n x ...
A book embedding of a graph consists of a linear ordering of the vertices along a line in 3-space (the spine), and an assignment of edges to half-planes with the spine as boundary (the pages), so that edges assigned to the same page can be drawn on that page without crossings. Given a graph G=(V,E), let f:V->N be a function such that 1=<f(v)=<deg(v). We present a Las Vegas algorithm which...
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