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**Equitable specialized block-colourings for Steiner triple systems.**
*(English)*
Zbl 1194.05012

Summary: We continue the study of specialized block-colourings of Steiner triple systems initiated by C.J. Colbourn and A. Rosa in [“Specialized block-colourings of Steiner triple systems and the upper chromatic index”, Graphs Comb. 19, No.3, 335–345 (2003; Zbl 1030.05017)] in which the triples through any element are coloured according to a given partition \(\pi \) of the replication number. Such colourings are equitable if \(\pi \) is an equitable partition (i.e., the difference between any two parts of \(\pi \) is at most one). Our main results deal with colourings according to equitable partitions into two, and three parts, respectively.

### Citations:

Zbl 1030.05017
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\textit{M. Gionfriddo} et al., Graphs Comb. 24, No. 4, 313--326 (2008; Zbl 1194.05012)

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### References:

[1] | Colbourn, C.J., Rosa, A.: Triple Systems (Oxford, 1999) · Zbl 0938.05009 |

[2] | Colbourn, C.J., Rosa, A.: Specialized block-colourings of Steiner triple systems and the upper chromatic index. Graphs Combin. 19, 335–345 (2003) · Zbl 1030.05017 |

[3] | Mendelsohn, E., Rosa, A.: Completing partial solutions to Heffter’s difference problem. Bull. Inst. Combin. Appl. (to appear) · Zbl 1201.05013 |

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