Distance-Preserving Subgraphs of Johnson Graphs

Victor Chepoi

doi:10.1007/s00493-016-3421-y

Distance-Preserving Subgraphs of Johnson Graphs

Victor Chepoi

Open Access

https://doi.org/10.1007/s00493-016-3421-y

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Journal: Combinatorica	Publication Date: Oct 24, 2016
Citations: 11

Affiliation: Laboratoire d’Informatique Fondamentale de Marseille, Aix-Marseille University, French National Centre for Scientific Research

#Johnson Graphs #Subsets Of Cardinality + Show 3 more

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Abstract

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. Djokovic [11] of distance-preserving subgraphs of hypercubes and provides an explicit description of the wallspace (split system) defining the embedding.

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