Seven criteria for integer sequences bring graphic
Journal of Graph Theory
On the comptational complexity of determining polyatomic structures by X-rays
Theoretical Computer Science
Reconstruction of domino tiling from its two orthogonal projections
Theoretical Computer Science
Reconstructing polyatomic structures from discrete X-rays: NP-completeness proof for three atoms
Theoretical Computer Science
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Reconstructing Polyatomic Structures from Discrete X-Rays: NP-Completeness Proof for Three Atoms
MFCS '98 Proceedings of the 23rd International Symposium on Mathematical Foundations of Computer Science
Tiling with bars under tomographic constraints
Theoretical Computer Science
On tiling under tomographic constraints
Theoretical Computer Science
Realizing disjoint degree sequences of span at most two: A tractable discrete tomography problem
Discrete Applied Mathematics
On the degree sequences of uniform hypergraphs
DGCI'13 Proceedings of the 17th IAPR international conference on Discrete Geometry for Computer Imagery
A formulation of the wide partition conjecture using the atom problem in discrete tomography
Discrete Applied Mathematics
Solving Multicolor Discrete Tomography Problems by Using Prior Knowledge
Fundamenta Informaticae - Strategies for Tomography
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We consider the problem of coloring a grid using $k$ colors with the restriction that each row and each column has a specific number of cells of each color. This problem has been known as the $(k-1)$-atom problem in the discrete tomography community. In an already classical result, Ryser obtained a necessary and sufficient condition for the existence of such a coloring when two colors are considered. This characterization yields a linear time algorithm for constructing such a coloring when it exists. Gardner et al. showed that for $k\geqslant 7$ the problem is NP-hard. Afterward Chrobak and Dürr improved this result by proving that it remains NP-hard for $k\geqslant 4$. We close the gap by showing that for $k=3$ colors the problem is already NP-hard. In addition, we give some results on tiling tomography problems.