... preceding it in the clockwise orientation and q the distance along the rimfrom np,κ. We place the following restriction on the spokes of the wheel, indicating thisthrough the subscripts of the spoke-nuts.Rule ... an upper bound for the function sat(n, Cl) that improves the upper bound given in [1] for most values of l. We improve the upper bound via several construc-tions. In our first construction ... acycle, Ro- the rim, of length sk for some s ≥ 4. Each kthvertex of the rim will be joinedby a spoke to one of the four vertices h1,h2,h3,h4 of the hub. We will, in the same fashionas above,...