Enumerations of (K_4-e)-designs with small orders

It is established that up to isomorphism,there are only one (K_4-e)-design of order 6, three (K_4-e)-designs of order 10 and two (K_4-e)-designs of order 11. As an application of our enumerative results, we discuss the fine triangle intersection problem for (K_4-e)-designs of orders v=6,10,11

The fine triangle intersections for maximum kite packings

In this paper the fine triangle intersection problem for a pair of maximum kite packings is investigated. Let Fin(v)={(s,t): $\exists$ a pair of maximum kite packings of order $v$ intersecting in $s$ blocks and $s+t$ triangles}. Let Adm(v)={(s,t): s+t\leq b_v, s,t are non-negative integers}, where $b_v=\lfloor v(v-1)/8\rfloor$. It is established that $Fin(v)= Adm(v)\setminus {(b_v-1,0),(b_v-1,1)}$ for any integer $v\equiv 0,1 ({\rm mod} 8)$ and $v\geq 8$; $Fin(v)=Adm(v)$ for any integer $v\equiv 2,3,4,5,6,7 ({\rm mod} 8)$ and $v\geq 4$