Abstract
Higman asked which block graphs of Steiner triple systems of order v satisfy the 4-vertex condition and left the cases v = 9, 13, 25 unsettled.We give a complete answer to this question by showing that the affine plane of order 3 and the binary projective spaces are the only such systems. The major part of the proof is to show that no block graph of a Steiner triple system of order 25 satisfies the 4-vertex condition.
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Communicated by L. Teirlinck.
P. R. J. Östergård formerly worked at Lehrstuhl Mathematik II, Universität Bayreuth, 95440 Bayreuth, Germany.
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Kaski, P., Khatirinejad, M. & Östergård, P.R.J. Steiner triple systems satisfying the 4-vertex condition. Des. Codes Cryptogr. 62, 323–330 (2012). https://doi.org/10.1007/s10623-011-9520-2
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DOI: https://doi.org/10.1007/s10623-011-9520-2