Embedding Cycles in Finite Planes
Digital Object Identifier (DOI)
Electronic Journal of Combinatorics
We define and study embeddings of cycles in finite affine and projective planes. We show that for all k, 3 ≤ k ≤ q2 , a k-cycle can be embedded in any affine plane of order q. We also prove a similar result for finite projective planes: for all k, 3 ≤ k ≤ q2 + q +1 , a k-cycle can be embedded in any projective plane of order q.
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Lazebnik, Felix, Keith E. Mellinger, and Oscar Vega. “Embedding Cycles in Finite Planes.” The Electronic Journal of Combinatorics 20, no. 3 (2013): 1–17. https://doi.org/10.37236/3377.