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Steiner triple systems satisfying the 4-vertex condition

机译:满足4顶点条件的Steiner三重系统

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摘要

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.
机译:Higman询问v阶Steiner三重系统的哪些框图满足4顶点条件,而v = 9,13,25的情况尚未解决。通过显示阶数为3的仿射平面和二元射影空间,我们给出了一个完整的答案,只有这样的系统。证明的主要部分是表明,阶数为25的Steiner三重系统的框图不满足4顶点条件。

著录项

  • 来源
    《Designs, Codes and Crytography》 |2012年第3期|p.323-330|共8页
  • 作者单位

    Department of Information and Computer Science, Helsinki Institute of Information Technology HIIT, Aalto University, P.O. Box 15400, 00076 Aalto, Finland;

    Department of Communications and Networking, Aalto University, P.O. Box 13000, 00076 Aalto, Finland,Department of Mathematics, University of British Columbia, 1984 Mathematics Road, Vancouver, BC V6T 1Z2, Canada;

    Department of Communications and Networking, Aalto University, P.O. Box 13000, 00076 Aalto, Finland;

  • 收录信息 美国《科学引文索引》(SCI);美国《工程索引》(EI);
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

    4-vertex condition; steiner triple system; strongly regular graph;

    机译:4顶点条件;斯坦纳三重系统强正则图;

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