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

A G ‐design is called embedded into an H ‐design if G is a subgraph of H and there is an injective mapping such that B is a subgraph of f ( B ) for every . In this paper, we determine that the necessary conditions for embedding a Steiner triple system into a Kite‐design are v ≡ 1, 3(mod 6), v + w ≡ 0, 1(mod 8), w ≥ ( v − 1)/6, and . 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.