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- Irina Mustata, Martin Pergel
- ArXiv
- 2013

It has been known since 1991 that the problem of recognizing grid intersection graphs is NP-complete. Here we use a modified argument of the above result to show that even if we restrict to the class of unit grid intersection graphs (UGIGs), the recognition remains hard, as well as for all graph classes contained inbetween. The result holds even when… (More)

- Irina Mustata, Kousuke Nishikawa, Asahi Takaoka, Satoshi Tayu, Shuichi Ueno
- Discrete Applied Mathematics
- 2016

- Stefan Felsner, George B. Mertzios, Irina Mustata
- MFCS
- 2013

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)

- Stefan Felsner, Irina Mustata, Martin Pergel
- SIAM J. Discrete Math.
- 2017

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)

- Felix Günther, Irina Mustata
- ArXiv
- 2013

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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