On the maximum double independence number of Steiner triple systems
نویسندگان
چکیده
منابع مشابه
On the Independence Number of Steiner Systems
A partial Steiner (n, r, l)-system is an r-uniform hypergraph on n vertices in which every set of l vertices is contained in at most one edge. A partial Steiner (n, r, l)-system is complete if every set of l vertices is contained in exactly one edge. In a hypergraph H, the independence number α(H) denotes the maximum size of a set of vertices in H containing no edge. In this article we prove th...
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Richard Wilson conjectured in 1974 the following asymptotic formula for the number of n-vertex Steiner triple systems: STS(n) = ( (1 + o(1)) n e2 )n2 6 . Our main result is that STS(n) ≤ ( (1 + o(1)) n e2 )n2 6 . The proof is based on the entropy method. As a prelude to this proof we consider the number F (n) of 1factorizations of the complete graph on n vertices. Using the KahnLovász theorem i...
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The upper chromatic number χ(H) of a set system H is the maximum number of colours that can be assigned to the elements of the underlying set of H in such a way that each H ∈ H contains a monochromatic pair of elements. We prove that a Steiner Triple System of order v ≤ 2 − 1 has an upper chromatic number which is at most k. This bound is the best possible, and the extremal configurations attai...
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Our main result is an existence and uniqueness theorem for Steiner triple systems which associates to every such system a binary code | called the \carrier" | which depends only on the order of the system and its 2-rank. When the Steiner triple system is of 2-rank less than the number of points of the system, the carrier organizes all the information necessary to construct directly all systems ...
متن کاملOn colourings of Steiner triple systems
A Steiner triple system, STS(v), is said to be χ-chromatic if the points can be coloured using χ colours, but no fewer, such that no block is monochromatic. All known 3-chromatic STS(v) are also equitably colourable, i.e. there exists a 3-colouring in which the cardinalities of the colour classes differ by at most one. We present examples of 3-chromatic STS(v) which do not admit equitable 3-col...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Designs
سال: 2020
ISSN: 1063-8539,1520-6610
DOI: 10.1002/jcd.21730