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6 votes
1 answer
143 views

Minimizing the number of segments in drawings of planar graphs

Every planar graph has at most $3n-6$ edges, where $n$ is the number of vertices. Moreover, every planar graph can be drawn with straight-line edges in the plane, without crossings. For example, for ...
3 votes
2 answers
1k views

maximum number of shortest path among a set of n triangle obstacles

Assume that we have a two distinct points. The number of shortest path between these two points is one. When we add a triangle obstacle to the plane and this triangle intersects the line connecting ...