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Gregarious GDDs with Two Associate Classes

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Abstract

The existence of group divisible designs with two associate classes has been studied for over 50 years. Probably the most difficult cases to solve are those in which the number of groups is less than the size of the blocks. Recently, such an existence problem was solved in the case where the groups have the same size and the blocks have size 3. In this paper, we continue to focus on blocks of size 3, solving the existence problem when the required designs are gregarious (each block intersects each group). These designs are tight to construct in the sense that they satisfy equality in one of the bounds required for GDDs to exist.

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Authors and Affiliations

  1. 4520 Mathematics Department, Illinois State University, Normal, IL, 61790-4520, USA

    Saad I. El-Zanati

  2. Department of Mathematics, Srinakharinwirot University, Sukhumvit 23, Bangkok, 10110, Thailand

    Narong Punnim

  3. Department of Mathematics and Statistics, Auburn University, 221 Parker Hall, Auburn, AL, 36849-5310, USA

    Chris A. Rodger

Authors
  1. Saad I. El-Zanati
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  2. Narong Punnim
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  3. Chris A. Rodger
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Corresponding author

Correspondence to Narong Punnim.

Additional information

This research was carried out under financial support from National Centre of Excellence in Mathematics, PERDO, Bangkok 10400, Thailand.

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El-Zanati, S.I., Punnim, N. & Rodger, C.A. Gregarious GDDs with Two Associate Classes. Graphs and Combinatorics 26, 775–780 (2010). https://doi.org/10.1007/s00373-010-0951-8

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  • DOI: https://doi.org/10.1007/s00373-010-0951-8

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