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Orthogonal ray graphs are the intersection graphs of horizontal and vertical rays (i.e. half-lines) in the plane. If the rays can have any possible orientation (left/right/up/down) then the graph is a 4-directional orthogonal ray graph (4-DORG). Otherwise, if all rays are only pointing into the positive x and y directions, the intersection graph is a(More)
The dimension of a partial order P is the minimum number of linear orders whose intersection is P. There are efficient algorithms to test if a partial order has dimension at most 2. In 1982 Yannakakis [24] showed that for k ≥ 3 to test if a partial order has dimension ≤ k is NP-complete. The height of a partial order P is the maximum size of a chain in P.(More)
We start with the well-known game below: Two players hold a sheet of paper to their forehead on which a positive integer is written. The numbers are consecutive and each player can only see the number of the other one. In each time step, they either say nothing or tell what number they have. Both of them will eventually figure out their number after a(More)
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