The fine triangle intersections for maximum kite packings. (English) Zbl 1263.05082
Summary: In this paper, the fine triangle intersection problem for a pair of maximum kite packings is investigated. Let \(\mathrm{Fin}(v)=\{(s,t): \exists\) a pair of maximum kite packings of order \(v\) intersecting in \(s\) blocks and \(s+t\) triangles\(\}\). Let \(\mathrm{Adm}(v)=\{(s,t): s+t \leq b_v,s,t\) are non-negative integers\(\}\), where \(b_v=\lfloor v(v-1)/8\rfloor\). It is established that \(\mathrm{Fin}(v)=\mathrm{Adm}(v)\backslash\{(b_v-1,0), (b_v-1,1)\}\) for any integer \(v\equiv 0,1 \pmod 8\) and \(v\geq 8; \mathrm{ Fin}(v)=\mathrm{Adm}(v)\) for any integer \(v \equiv 2,3,4,5,6,7 \pmod 8\) and \(v \geq 4\).
MSC:
| 05C70 | Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.) |
| 05B05 | Combinatorial aspects of block designs |
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