A simple characterization of the 3, 4, or 5-colorable Eulerian triangulations of the projective plane is given. Key words: Projective plane, triangulation, coloring, Eulerian grap...
We show that for any closed surface F with χ(F) −4 (or χ(F) −2), there exist graphs that triangulate the torus or the Klein bottle (or the projective plane) and that quadran...
We present a polynomial-time approximation scheme (PTAS) for the Steiner tree problem with polygonal obstacles in the plane with running time O(n log2 n), where n denotes the numb...
In a rooted graph, a vertex is designated as its root. An outerplanar graph is represented by a plane embedding such that all vertices appear along its outer boundary. Two differ...
An algorithm is presented for the geometric analysis of an algebraic curve f(x, y) = 0 in the real affine plane. It computes a cylindrical algebraic decomposition (CAD) of the pla...