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- W3105596242 abstract "We consider embeddings of 3-regular graphs into 3-dimensional Cartesian coordinates, in such a way that two vertices are adjacent if and only if two of their three coordinates are equal (that is, if they lie on an axis-parallel line) and such that no three points lie on the same axis-parallel line; we call a graph with such an embedding an xyz graph}. We describe a correspondence between xyz graphs and face-colored embeddings of the graph onto two-dimensional manifolds, and we relate bipartiteness of the xyz graph to orientability of the underlying topological surface. Using this correspondence, we show that planar graphs are xyz graphs if and only if they are bipartite, cubic, and three-connected, and that it is NP-complete to determine whether an arbitrary graph is an xyz graph. We also describe an algorithm with running time O(n 2^{n/2}) for testing whether a given graph is an xyz graph." @default.
- W3105596242 created "2020-11-23" @default.
- W3105596242 creator A5048574995 @default.
- W3105596242 date "2013-01-01" @default.
- W3105596242 modified "2023-09-27" @default.
- W3105596242 title "The Complexity of Bendless Three-Dimensional Orthogonal Graph Drawing" @default.
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- W3105596242 doi "https://doi.org/10.7155/jgaa.00283" @default.
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