To the theory of \(q\)-ary Steiner and other-type trades
We introduce the concept of a clique bitrade, which generalizes several known types of bitrades, including latin bitrades, Steiner \(T(k-1,k,v)\) bitrades, extended \(1\)-perfect bitrades. For a distance-regular graph, we show a one-to-one correspondence between the clique bitrades that meet the wei...
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Veröffentlicht in: | arXiv.org 2015-08 |
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Format: | Artikel |
Sprache: | eng |
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Zusammenfassung: | We introduce the concept of a clique bitrade, which generalizes several known types of bitrades, including latin bitrades, Steiner \(T(k-1,k,v)\) bitrades, extended \(1\)-perfect bitrades. For a distance-regular graph, we show a one-to-one correspondence between the clique bitrades that meet the weight-distribution lower bound on the cardinality and the bipartite isometric subgraphs that are distance-regular with certain parameters. As an application of the results, we find the minimum cardinality of \(q\)-ary Steiner \(T_q(k-1,k,v)\) bitrades and show a connection of minimum such bitrades with dual polar subgraphs of the Grassmann graph \(J_q(v,k)\). Keywords: bitrades, trades, Steiner systems, subspace designs |
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ISSN: | 2331-8422 |
DOI: | 10.48550/arxiv.1412.3792 |