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

Yufeng Gao

Journal of Mathematics, 2025, vol. 2025, 1-16

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.

Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jjmath:3621902

DOI: 10.1155/jom/3621902

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