摘要:
Let (X,B) be a λ-fold K1,4-design of order v.For each block B =(a:b,c,d,e) ∈B,if we remove the edge {a,e},we have a K1,a [a:b,c,d].Let C be the collection of K1,3s obtained by removing an edge of each block of B,and F be the collection of the deleted edges.If Fr can be reassembled into a collection D of [λv(v-1)/24] K1,3s,then (X,C ∪ D) is a maximum λ-fold K1,3-packing of order v.We call (X,C ∪ D) a metamorphosis of the λ-fold K1,4-design (X,B).In this paper,we show that there exists a metamorphosis of a λ-fold K1,4-design of order v into a maximum λ-fold K1,3-packing of order v if and only if λv(v-1)=0 (mod 8) and v ≥ 5.%令(X,B)为一个v阶的λ-重K1,4-设计.对于每一个区组B=(a:b,c,d,e)∈B,若删去边{a,e},则得到一个K1,3[a:b,c,d].令C为删去B中每一个区组的边{a,e}而得到的K1,3的集合,F为被删去的边构成的集合.若F可以被重组成[λv(v-1)/24]个K1,3的集合D,则(X,C ∪D)为一个v阶λ-重K1,3-最大填充.称(X,C∪D)为λ-重K1,4-设计(X,B)的变形.本文证明了v阶λ-重K1,4-设计到v阶λ-重K1,3-最大填充的变形存在的充要条件是λv(v-1)兰0(mod 8)且v≥5.