Extended 5-Cycle Systems

Abstract

An extended 5-cycle system of order $n$ is an ordered pair $(V,B)$, where $B$ is a collection of edge-disjoint 5-cycles, 2-tadpoles, and loops that partition the edges of the graph $K_n^{+}$ whose vertex set is an $n$-set $V$. In this paper, we show that an extended 5-cycle system of order $n$ exists for all $n$ except $n=2$ and $3$.