Completing the spectrum of almost resolvable cycle systems with odd cycle length

TL;DR

This paper constructs almost resolvable cycle systems of order 4k+1 for odd k≥11, completing the existence proof for such systems with odd cycle lengths.

Contribution

It provides the first construction for almost resolvable cycle systems with odd cycle length for all sufficiently large odd k.

Findings

Established existence of almost resolvable cycle systems for all odd k≥11.

Extended the spectrum of known cycle systems to include new odd cycle lengths.

Contributed to the theory of combinatorial design by completing a key existence problem.

Abstract

In this paper, we construct almost resolvable cycle systems of order $4k+1$ for odd $k\ge 11$. This completes the proof of the existence of almost resolvable cycle systems with odd cycle length.