We study straight-line drawings of graphs with few segments and few slopes. Optimal results are obtained for all trees. Tight bounds are obtained for outerplanar graphs, 2-trees, a...
A set of vertices C in a graph is convex if it contains all vertices which lie on shortest paths between vertices in C. The convex hull of a set of vertices S is the smallest conve...
Abstract. CrossingNumber is one of the most challenging algorithmic problems in topological graph theory, with applications to graph drawing and VLSI layout. No polynomial time con...
A D-polyhedron is a polyhedron P such that if x, y are in P then so are their componentwise max and min. In other words, the point set of a D-polyhedron forms a distributive latti...
For a bounded integer , we wish to color all edges of a graph G so that any two edges within distance have different colors. Such a coloring is called a distance-edge-coloring or ...