Spanning sets and scattering sets in Steiner triple systems
نویسندگان
چکیده
A spanning set in a Steiner triple system is a set of elements for which each element not in the spanning set appears in at least one triple with a pair of elements from the spanning set. A scattering set is a set of elements that is independent, and for which each element not in the scattering set is in at most one triple with a pair of elements from the scattering set. For each v = 1,3 (mod 6), we exhibit a Steiner triple system with a spanning set of minimum cardinality, and a Steiner triple system with a scattering set of maximum cardinality. In the process, we establish the existence of Steiner triple systems with complete arcs of the minimum possible cardinality.
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عنوان ژورنال:
- J. Comb. Theory, Ser. A
دوره 57 شماره
صفحات -
تاریخ انتشار 1991