Octagon kite systems

Electronic Notes in Discrete Mathematics

Volume 40, 15 May 2013, Pages 129-134

The spectrum of octagon kite system (OKS) which is nesting strongly balanced 4-kite-designs is determined.

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On the existence of uniformly resolvable decompositions of K<inf>v</inf> and K<inf>v</inf> - I into paths and kites
2013, Discrete Mathematics
In this paper, it is shown that, for every $v \equiv 0 (mod 12)$ , there exists a uniformly resolvable decomposition of $K_{v}$ - $I$ , the complete undirected graph minus a $1$ -factor, into $r$ classes containing only copies of 2-stars and $s$ classes containing only copies of kites if and only if $(r, s) \in {(3 x, 1 + \frac{v - 4}{2} - 2 x), x = 0, \dots, \frac{v - 4}{4}}$ . It is also shown that a uniformly resolvable decomposition of $K_{v}$ into $r$ classes containing only copies of 2-stars and $s$ classes containing only copies of kites exists if and only if $v \equiv 9 (mod 12)$ and $s = 0$ .
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