Metamorphosis of fold P5-designs into maximum of fold P4-packings

Abstract

Let (X} B) he a -fold P5-design of order v. For each block B = (a, 6, c, d) e) € B, if we remove the edge {d, e}, we have a P4 [a, b, c, d]. Let C he the collection of P4s obtained by removing an edge of each block of B, and F be the collection of the deleted edges. If F can be reassembled into a collection D of l)/24J P4S, then (X ,CUT>) is a maximum fold p4 packing of order v. We call (X C u D) is a metamorphosis of the fold P5-design (X} B). In this paper, we show that there exists a metamorphosis of a A-fold Ps-design of order v into a maximum fold p4 -packing of order v if and only if t;(v - 1) = 0 (mod 8) and v≥5. © 2018 Utilitas Mathematica Publishing Incorporated. All rights reserved.