On Orthogonal Double Covers of $K_n$

Abstract

An orthogonal double cover of the complete graph $K_n$ is a collection of $n$ spanning subgraphs $G_1,G_2,\dots ,G_n\$of\text{(}{K}_n$ such that every edge of $K_n$ belongs to exactly 2 of the $G_i$’s and every pair of $G_i$s intersect in exactly one edge.
It is proved that an orthogonal double cover exists for all $n\ge 4$, where the $G_i$’s consist of short cycles; this result also proves a conjecture of Chung and West.