Abstract
We test in polynomial time whether a graph embeds in a distance-preserving way into the hexagonal tiling, the three-dimensional diamond structure, or analogous higher-dimensional structures.
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Balaban, A.T.: Graphs of multiple 1, 2-shifts in carbonium ions and related systems. Rev. Roum. Chim. 11, 1205 (1966)
Bhatt, S., Cosmodakis, S.: The complexity of minimizing wire lengths in VLSI layouts. Inform. Proc. Lett. 25, 263–267 (1987)
Dilworth, R.P.: A decomposition theorem for partially ordered sets. Annals of Mathematics 51, 161–166 (1950)
Djokovic, D.Z.: Distance preserving subgraphs of hypercubes. J. Combinatorial Theory, Ser. B 14, 263–267 (1973)
Eades, P., Whitesides, S.: The logic engine and the realization problem for nearest neighbor graphs. Theoretical Computer Science 169(1), 23–37 (1996)
Eppstein, D.: Algorithms for drawing media. In: Pach, J. (ed.) GD 2004. LNCS, vol. 3383, pp. 173–183. Springer, Heidelberg (2005)
Eppstein, D.: The lattice dimension of a graph. Eur. J. Combinatorics 26(5), 585–592 (July 2005), http://dx.doi.org/10.1016/j.ejc.2004.05.001
Eppstein, D.: Cubic partial cubes from simplicial arrangements. Electronic J. Combinatorics 13(1), R79 (2006)
Eppstein, D.: Recognizing partial cubes in quadratic time. In: Proc. 19th Symp. Discrete Algorithms, pp. 1258–1266. ACM and SIAM (2008)
Eppstein, D.: The topology of bendless three-dimensional orthogonal graph drawing. In: Proc. 16th Int. Symp. Graph Drawing (2008)
Eppstein, D., Falmagne, J.C., Ovchinnikov, S.: Media Theory: Applied Interdisciplinary Mathematics. Springer, Heidelberg (2008)
Felsner, S., Raghavan, V., Spinrad, J.: Recognition algorithms for orders of small width and graphs of small Dilworth number. Order 20(4), 351–364 (2003)
Mislow, K.: Role of pseudorotation in the stereochemistry of nucleophilic displacement reactions. Acc. Chem. Res. 3(10), 321–331 (1970)
Winkler, P.: Isometric embeddings in products of complete graphs. Discrete Applied Mathematics 7, 221–225 (1984)
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Eppstein, D. (2009). Isometric Diamond Subgraphs. In: Tollis, I.G., Patrignani, M. (eds) Graph Drawing. GD 2008. Lecture Notes in Computer Science, vol 5417. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-00219-9_37
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DOI: https://doi.org/10.1007/978-3-642-00219-9_37
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-00218-2
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