Distance-Preserving Subgraphs of Johnson Graphs


We give a characterization of distance-preserving subgraphs of Johnson graphs, i.e., of graphs which are isometrically embeddable into Johnson graphs (the Johnson graph J(m,∧) has the subsets of cardinality m of a set ∧ as the vertex-set and two such sets A,B are adjacent iff |AΔB|=2). Our characterization is similar to the characterization of D. Ž. Djoković [11] of distance-preserving subgraphs of hypercubes and provides an explicit description of the wallspace (split system) defining the embedding.

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Correspondence to Victor Chepoi.

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Chepoi, V. Distance-Preserving Subgraphs of Johnson Graphs. Combinatorica 37, 1039–1055 (2017). https://doi.org/10.1007/s00493-016-3421-y

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Mathematics Subject Classification (2000)

  • 05C12
  • 52B40