Abstract
A symmetric rank two tactical configuration is a regular bi-partite graph of girth 6. If it is (n+1)-regular on 2(n2+n+1+k) points it is denoted T(n,k). There is a polynomial, P(n) ≈ n4, such that T(n, k) exist for all k > P(n). This paper discusses the cases k < P(n), and some methods for finding such "small" T(n,k), including computational methods and the use of difference sets.
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References
Hall, M., Jr., Cyclic Projective Planes, Duke Mathematical Journal, Vol. 14 (1947), 1079–1090.
Longyear, J. Q., Tactical Configurations. Doctoral Dissertation, Pennsylvania State University (1972).
Payne, S. E., On the Non-Existence of a Class of Configurations Which are Nearly Generalized n-Gons, J. Combinatorial Theory, 12 (1972), 268–282.
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© 1974 Springer-Verlag Berlin
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Limpan, M.J. (1974). The existence of small tactical configurations. In: Bari, R.A., Harary, F. (eds) Graphs and Combinatorics. Lecture Notes in Mathematics, vol 406. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0066453
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DOI: https://doi.org/10.1007/BFb0066453
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