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The Embedding Problem of Any Steiner Triple Systems Into Kite-Designs

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  • Yufeng Gao

Abstract

A G-design V,B is called embedded into an H-design V∪W,C if G is a subgraph of H and there is an injective mapping f:B⟶C such that B is a subgraph of fB for every B∈B. In this paper, we determine that the necessary conditions for embedding a Steiner triple system V,B into a Kite-design V∪W,C are v≡1,3mod 6, v+w≡0,1mod 8, w≥v−1/6, and 1/4w2≤1/4v+w2−1/3v2≤w2. We show that the necessary conditions are sufficient for the second minimal V∪W. The results have potential applications in optimizing resource allocation for two-period optical networks and improving grooming efficiency in wavelength-division multiplexing (WDM) systems.

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  • Yufeng Gao, 2025. "The Embedding Problem of Any Steiner Triple Systems Into Kite-Designs," Journal of Mathematics, Hindawi, vol. 2025, pages 1-16, April.
    • Handle: RePEc:hin:jjmath:3621902
    DOI: 10.1155/jom/3621902
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