A local characterization of the johnson scheme

Abstract

Within the Johnson schemeI(m, d) we find the graphK(m, d) ofd-subsets of anm-set, two such adjacent when disjoint. Among all connected graphs,K(m, d) is characterized by the isomorphism type of its vertex neighborhoods providedm is sufficiently large compared tod.

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Partial support provided by NSF (USA), SERC (UK), ZWO (NL).

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Hall, J.I. A local characterization of the johnson scheme. Combinatorica 7, 77–85 (1987). https://doi.org/10.1007/BF02579203

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AMS subject classification (1980)

  • 05 B 30