On the directed Oberwolfach problem for complete symmetric equipartite digraphs and uniform-length cycles

2023/03/08 by Nevena Francetić, Francetić, Nevena, Mateja Šajna +1
Biochemistry, Genetics and Molecular Biology · Engineering · Mathematics · #05C51 #05C70 #Combinatorics (math.CO) #DNA and Nucleic Acid Chemistry #FOS: Mathematics #Finite Group Theory Research #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.2303.04308

openalex publication_date 2023/03/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We examine the necessary and sufficient conditions for a complete symmetric equipartite digraph K_n[m]^∗ with n parts of size m to admit a resolvable decomposition into directed cycles of length t. We show that the obvious necessary conditions are sufficient for m,n,t ≥ 2 in each of the following four cases: (i) m(n-1) is even; (ii) gcd(m,n) \not∈ \1,3\; (iii) gcd(m,n)=1 and 4|n or 6|n; and (iv) gcd(m,n)=3, and if n=6, then p|m for a prime p ≤ 37.

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