Classification of subsets with minimal width and dual width in Grassmann, bilinear forms and dual polar graphs

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34 Citations (Scopus)

Abstract

Brouwer, Godsil, Koolen and Martin [Width and dual width of subsets in polynomial association schemes, J. Combin. Theory Ser. A 102 (2003) 255-271] introduced the width w and the dual width w* of a subset in a distance-regular graph and in a cometric association scheme, respectively, and then derived lower bounds on these new parameters. For instance, subsets with the property w + w* = d in a cometric distance-regular graph with diameter d attain these bounds. In this paper, we classify subsets with this property in Grassmann graphs, bilinear forms graphs and dual polar graphs. We use this information to establish the Erdo{combining double acute accent}s-Ko-Rado theorem in full generality for the first two families of graphs.

Original languageEnglish
Pages (from-to)903-910
Number of pages8
JournalJournal of Combinatorial Theory. Series A
Volume113
Issue number5
DOIs
Publication statusPublished - 2006 Jul 1

Keywords

  • Association scheme
  • Distance-regular graph
  • Erdo{combining double acute accent}s-Ko-Rado theorem

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics

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