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 sequenc-ing. We prove that 3-good sequencings exist for any STS(v) with v>3 and 4-good sequencings exist for any STS(v) with v>71. Similar re-sults 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.
AUSTRALASIAN JOURNAL OF COMBINATORICS
Kreher, D. L.,
Stinson, D. R.
Block-avoiding sequencings of points in Steiner triple systems.
AUSTRALASIAN JOURNAL OF COMBINATORICS,
Retrieved from: https://digitalcommons.mtu.edu/michigantech-p/600
Creative Commons License
This work is licensed under a Creative Commons Attribution-No Derivative Works 4.0 International License.
© The author(s). Released under the CC BY-ND 4.0 International License. Publisher’s version of record: http://ajc.maths.uq.edu.au/pdf/74/ajc_v74_p498.pdf