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The 3-Way Intersection Problem for Kite Systems

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Abstract

In this paper we introduce the 3-way intersection problem for G-designs, and we consider this problem for kite systems. Let \(b_v=v(v-1)/8\) and \(I_3(v)=\{0,1,\ldots ,b_v\}{\setminus }\{b_v-1\}\). Let \(J_3(v)=\{s:\) there exist three kite systems of order v intersecting in s blocks\(\}\). We show that for any positive integer \(v\equiv 0,1\pmod {8}\) and \(v\ge 8\), \(J_3(v)=I_3(v)\).

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Acknowledgements

The authors would like to thank the referees for their valuable suggestions to improve the readability of this paper. This work was supported by Zhejiang Provincial Natural Science Foundation of China under Grant LY17A010008, NSFC under Grants 11771227, 11871291, and K.C. Wong Magna Fund in Ningbo University.

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Authors and Affiliations

  1. Department of Mathematics, Ningbo University, Ningbo, 315211, People’s Republic of China

    Ping Chen & Xiaomiao Wang

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  1. Ping Chen
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  2. Xiaomiao Wang
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Correspondence to Xiaomiao Wang.

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Chen, P., Wang, X. The 3-Way Intersection Problem for Kite Systems. Graphs and Combinatorics 34, 1741–1749 (2018). https://doi.org/10.1007/s00373-018-1976-7

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  • DOI: https://doi.org/10.1007/s00373-018-1976-7

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