Department of Mathematical Sciences
Given an STS(v), we ask if there is a permutation of the points of the design such that no L consecutive points in this permutation contain a block of the design. Such a permutation is called an L-good sequencing. We prove that 3-good sequencings exist for any STS(v) with v>3and 4-good sequencings exist for any STS(v) with v>71. Similar results also hold for partial STS(v). Finally, we determine the existence or nonexistence of 4-good sequencings for all the nonisomorphic STS(v) with v=7,9,13 and 15.
The Australasian Journal of Combinatorics
Kreher, D. L.,
Stnson, D. R.
Block-avoiding sequencings of points in Steiner triple systems.
The Australasian Journal of Combinatorics,
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