Almost 2-perfect 8-cycle systems

2017/10/23 by Selda Küçükçifçi, Küçükçifçi, Selda, Charles Curtis Lindner +5
Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #math.CO

paper · pdf · doi:10.48550/arxiv.1710.08265

arxiv created 2017/10/23 · arxiv updated 2017/10/24

Abstract

For an m-cycle C, an inside m-cycle of C is a cycle on the same vertex set, that is edge-disjoint from C. In an m-cycle system, (X, C), if inside m-cycles can be chosen -one for each cycle- to form another m-cycle system, then (X, C) is called an almost 2-perfect m-cycle system. Almost 2-perfect cycle systems can be considered as generalisations of 2-perfect cycle systems. Cycle packings are generalisations of cycle systems that allow to have leaves after decomposition. In this paper, we prove that an almost 2-perfect maximum packing of K_n with 8-cycles of order n exists for each n≥ 8. We also construct a maximum 8-cycle packing of order n which is not almost 2-perfect for each n ≥ 10.

Related

• Cycle packings of the complete multigraph
• On the existence of unparalleled even cycle systems
• Improved bound on the number of cycle sets
• Completing the spectrum of almost resolvable cycle systems with odd cycle length
• m-Cycle Packings of (λ+μ)K_v+u-λK_v: m even