We study straight-line drawings of planar graphs with few segments and few slopes. Optimal
results are obtained for all trees. Tight bounds are obtained for outerplanar graphs, 2-trees …

The geometric thickness of a graph G is the minimum integer k such that there is a straight
line drawing of G with its edge set partitioned into k plane subgraphs. Eppstein [Separating …

" Based on a lecture series given by the authors at a satellite meeting of the 2006
International Congress of Mathematicians and on many articles written by them and their …

We define a simple orthogonal polyhedron to be a three-dimensional polyhedron with the
topology of a sphere in which three mutually-perpendicular edges meet at each vertex. By …

We prove that the stack-number of the strong product of three n-vertex paths is Θ (n 1/3). The
best previously known upper bound was O (n). No non-trivial lower bound was known. This …

We settle a problem of Dujmović, Eppstein, Suderman, and Wood by showing that there
exists a function f with the property that every planar graph G with maximum degree d admits …

It is known that every planar graph has a planar embedding where edges are represented
by non-crossing straight-line segments. We study the planar slope number, ie, the minimum …

In a dispersable book embedding, the vertices of a given graph G must be ordered along a
line ℓ, called spine, and the edges of G must be drawn in different half-planes bounded by ℓ …

The planar slope number of a planar graph $ G $ is defined as the minimum number of
slopes that is required for a crossing-free straight-line drawing of $ G $. We show that …

The slope-number of a graph G is the minimum number of distinct edge slopes in a straight-
line drawing of G in the plane. We prove that for Δ⩾ 5 and all large n, there is a Δ-regular n …