To the theory of $q$-ary Steiner and other-type trades

Discrete Math. 339(3) 2016, 1150-1157 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...

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Hauptverfasser: Krotov, Denis, Mogilnykh, Ivan, Potapov, Vladimir
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Sprache:eng
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Zusammenfassung:Discrete Math. 339(3) 2016, 1150-1157 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
DOI:10.48550/arxiv.1412.3792