Embedding cycles in finite planes

2013/05/12 by Felix Lazebnik, Lazebnik, Felix, Keith E. Mellinger +3
Engineering · Mathematics · #51 #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #Limits and Structures in Graph Theory #Primary 05 #Secondary 20 #graph theory and CDMA systems #math.CO #msc:05 #msc:20 #msc:51

paper · pdf · doi:10.48550/arxiv.1305.2646

15 pages, 10 figures

arxiv created 2013/05/12 · openalex publication_date 2013/05/12 · arxiv updated 2013/05/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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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