2021/08/02 by Adrián Vázquez-Ávila, Vázquez-Ávila, Adrián
Engineering · Mathematics · #Advanced Mathematical Theories #Combinatorics (math.CO) #FOS: Mathematics #Mathematics and Applications #graph theory and CDMA systems #math.CO
paper · pdf · doi:10.48550/arxiv.2108.01209
arXiv admin note: text overlap with arXiv:1906.09291
arxiv created 2021/08/02 · openalex publication_date 2021/08/02 · arxiv updated 2021/08/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
An one-factorization F of the complete graph Kn is (l,Ck), where l≥0 and k≥4 are integers, if the union F∪ G, for any F,G\inF, includes exactly l (edge-disjoint) cycles of length k (lk≤ n). Moreover, a pair of orthogonal one-factorizations F and G of the complete graph Kn is (l,Ck) if the union F∪ G, for any F\inF and G\inG, includes exactly l cycles of length k. In this paper, we prove the following: if q≡11 (mod 24) is an odd prime power, then there is a (1,C4) one-factorization of Kq+1. Also, there is a pair of orthogonal (2,C4) one-factorization of Kq+1.