| Budget Amount *help |
¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000)
Fiscal Year 2015: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2014: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2013: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2012: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
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| Outline of Final Research Achievements |
A graph is said to be 1-planar (or 1-embedding of a closed surface) if the graph can be drawn on the sphere (or the surface) so that each edge has at most one crossing point with another edge. In this research, we discuss 1-planar graphs (or 1-embeddings of closed surfaces) from the viewpoint of “re-embeddings”of those graphs, and obtained some results around this topic, which are clearly different from past results. In particular, in the joint work with Prof. Eades in Australia, we had shown that the problem of testing maximal 1-planarity of a graph can be solved in linear time, if a rotation system is given. Furthermore, we could prove that there exists no optimal 1-planar graph which can triangulate a non-orientable surface.
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