Partial cubes: structures, characterizations, and constructions - Mathematics CombinatoricsReport as inadecuate




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Abstract: Partial cubes are isometric subgraphs of hypercubes. Structures on a graphdefined by means of semicubes, and Djokovi\{c}s and Winklers relations playan important role in the theory of partial cubes. These structures are employedin the paper to characterize bipartite graphs and partial cubes of arbitrarydimension. New characterizations are established and new proofs of some knownresults are given.The operations of Cartesian product and pasting, and expansion andcontraction processes are utilized in the paper to construct new partial cubesfrom old ones. In particular, the isometric and lattice dimensions of finitepartial cubes obtained by means of these operations are calculated.



Author: Sergei Ovchinnikov

Source: https://arxiv.org/







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