Abstract
A cut-complex over the geometric n-cube is an induced subgraph of the cube whose vertices are strictly separated from the rest of the cube by a hyperplane of R n. A cut is the set of all the edges connecting the cut-complex to its node-complement subgraph. Here, we will extend the concepts of hyperplane cuts and cut-complexes to a larger class of cubical graphs called c-cuts, and c-complexes respectively. Then, we prove connectivity of the c-complexes that is essential for their characterization. Finally, we outline new open problems regarding the c-cuts and c-complexes over the n-cube.
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Emamy-Khansary, M.R. (2011). Cuts, c-Cuts, and c-Complexes over the n-Cube. In: Pahl, J., Reiners, T., Voß, S. (eds) Network Optimization. INOC 2011. Lecture Notes in Computer Science, vol 6701. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21527-8_67
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DOI: https://doi.org/10.1007/978-3-642-21527-8_67
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