Almost resolvable k-cycle systems with k≡ 2\pmod 4

2017/09/25 by L. Wang, H. Cao, Wang, L. +1
Computer Science · Engineering · Mathematics · #Coding theory and cryptography #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #graph theory and CDMA systems #math.CO

paper · pdf · doi:10.48550/arxiv.1710.00647

cycle system; almost resolvable cycle system. arXiv admin note: substantial text overlap with arXiv:1706.05958, arXiv:1605.00818

openalex publication_date 2017/09/25 · arxiv created 2018/04/27 · arxiv updated 2018/04/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we show that if k≥ 6 and k ≡ 2 \pmod 4, then there exists an almost resolvable k-cycle system of order 2kt+1 for all t≥ 1 except possibly for t=2 and k≥ 14. Thus we give a partial solution to an open problem posed by Lindner, Meszka, and Rosa (J. Combin. Des., vol. 17, pp.404-410, 2009).

Citations

• Completing the spectrum of almost resolvable cycle systems with odd cycle length
• Further results on the Hamilton-Waterloo problem

Related

• Completing the spectrum of almost resolvable cycle systems with odd cycle length
• Almost resolvable even cycle systems of (K_u × K_g)(λ)
• On the existence of unparalleled even cycle systems
• Further results on the Hamilton-Waterloo problem
• Almost 2-perfect 8-cycle systems