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167
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DM
2002
186views more  DM 2002»
15 years 3 months ago
Coloring Eulerian triangulations of the projective plane
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...
Bojan Mohar
JCT
2007
142views more  JCT 2007»
15 years 3 months ago
Graphs that triangulate a given surface and quadrangulate another surface
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...
Yusuke Suzuki
155
Voted
WADS
2007
Springer
165views Algorithms» more  WADS 2007»
15 years 9 months ago
A Near Linear Time Approximation Scheme for Steiner Tree Among Obstacles in the Plane
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...
Matthias Müller-Hannemann, Siamak Tazari
148
Voted
IEICET
2011
14 years 10 months ago
Generation of Symmetric and Asymmetric Biconnected Rooted Outerplanar Graphs
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...
Bingbing Zhuang, Hiroshi Nagamochi
118
Voted
ISSAC
2007
Springer
146views Mathematics» more  ISSAC 2007»
15 years 9 months ago
Fast and exact geometric analysis of real algebraic plane curves
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...
Arno Eigenwillig, Michael Kerber, Nicola Wolpert