Embedding cycles in finite planes (Q396840)

Summary: We define and study embeddings of cycles in finite affine and projective planes. We show that for all \(k\), \(3\leq k\leq q^2\), 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 \(k\), \(3\leq k\leq q^2+q+1\), a \(k\)-cycle can be embedded in any projective plane of order \(q\).