Cyclic $m$-cycle systems of complete graphs minus a 1-factor

TL;DR

This paper establishes precise conditions for the existence of cyclic m-cycle decompositions of complete graphs minus a 1-factor, focusing on cases where both m and n are even and m divides n.

Contribution

It provides necessary and sufficient conditions for cyclic m-cycle systems of K_n minus a 1-factor under specific parity and divisibility constraints.

Findings

Necessary and sufficient conditions derived for cyclic m-cycle systems

Conditions specifically for even m and n with m dividing n

Advances understanding of cycle decompositions in complete graphs

Abstract

In this paper, we provide necessary and sufficient conditions for the existence of a cyclic $m$-cycle system of $K_n-I$ when $m$ and $n$ are even and $m \mid n$.