Isometric Diamond Subgraphs [chapter]

David Eppstein
2009 Lecture Notes in Computer Science  
We test in polynomial time whether a graph embeds in a distancepreserving way into the hexagonal tiling, the three-dimensional diamond structure, or analogous higher-dimensional structures. Hexagons and Diamonds from Slices of Lattices The three-dimensional points {(x, y, z) | x+y+z ∈ {0, 1}}, with edges connecting points at unit distance, form a 3-regular infinite graph (Fig. 1, left) in which every vertex has I.G. Tollis and M.
doi:10.1007/978-3-642-00219-9_37 fatcat:5rascgkdnffwrlwmgxf2vaz3a4