Tribes of Cubic Partial Cubes

Classification of vertex-transitive cubic partial cubes

Partial cubes are graphs isometrically embeddable into hypercubes. In this paper it is proved that every cubic, vertex-transitive partial cube is isomorphic to one of the following graphs: K2ƒC2n, for some n ≥ 2, generalized Petersen graph G(10, 3), permutahedron, truncated cuboctahedron, or truncated icosidodecahedron. This complete classification of cubic, vertex-transitive partial cubes, a f...

Cubic Partial Cubes from Simplicial Arrangements

We show how to construct a cubic partial cube from any simplicial arrangement of lines or pseudolines in the projective plane. As a consequence, we find nine new infinite families of cubic partial cubes as well as many sporadic examples.

On cubic and edge-critical isometric subgraphs of hypercubes

All cubic partial cubes (i.e., cubic isometric subgraphs of hypercubes) up to 30 vertices and all edge-critical partial cubes up to 14 vertices are presented. The lists of graphs were confirmed by computer search to be complete. Non-trivial cubic partial cubes on 36, 42, and 48 vertices are also constructed.

Cubic inflation, mirror graphs, regular maps, and partial cubes

Universitet Cubical local partial orders on cubically subdivided spaces - existence and construction

The geometric models of Higher Dimensional Automata and Dijkstra’s PV-model are cubically subdivided topological spaces with a local partial order. If a cubicalization of a topological space is free of immersed cubic Möbius bands, then there are consistent choices of direction in all cubes, such that any n-cube in the cubic subdivision is dihomeomorphic to [0, 1]n with the induced partial order...