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Equitable Specialized Block-Colourings for Steiner Triple Systems

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Abstract

We continue the study of specialized block-colourings of Steiner triple systems initiated in [2] in which the triples through any element are coloured according to a given partition π of the replication number. Such colourings are equitable if π is an equitable partition (i.e., the difference between any two parts of π is at most one). Our main results deal with colourings according to equitable partitions into two, and three parts, respectively.

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References

  1. Colbourn, C.J., Rosa, A.: Triple Systems (Oxford, 1999)

  2. Colbourn, C.J., Rosa, A.: Specialized block-colourings of Steiner triple systems and the upper chromatic index. Graphs Combin. 19, 335–345 (2003)

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  3. Mendelsohn, E., Rosa, A.: Completing partial solutions to Heffter’s difference problem. Bull. Inst. Combin. Appl. (to appear)

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Authors and Affiliations

  1. University of Catania, Catania, Italy

    Mario Gionfriddo & Lorenzo Milazzo

  2. University of Washington, Tacoma, WA, USA

    Peter Horák

  3. McMaster University, Hamilton, ON, Canada

    Alex Rosa

Authors
  1. Mario Gionfriddo
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  2. Peter Horák
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  3. Lorenzo Milazzo
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  4. Alex Rosa
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Gionfriddo, M., Horák, P., Milazzo, L. et al. Equitable Specialized Block-Colourings for Steiner Triple Systems. Graphs and Combinatorics 24, 313–326 (2008). https://doi.org/10.1007/s00373-008-0794-8

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  • DOI: https://doi.org/10.1007/s00373-008-0794-8

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