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Extensions of Steiner Triple Systems [PDF]
Journal of Combinatorial DesignsABSTRACTIn this article, we study extensions of Steiner triple systems by means of the associated Steiner loops. We recognize that the set of Veblen points of a Steiner triple system corresponds to the center of the Steiner loop. We investigate extensions of Steiner loops, focusing in particular on the case of Schreier extensions, which provide a ...
Giovanni Falcone +2 more
exaly +4 more sources
High-girth Steiner triple systems
Annals of MathematicsWe prove a 1973 conjecture due to Erdős on the existence of Steiner triple systems with arbitrarily high girth.
Matthew Kwan +2 more
exaly +6 more sources
Embedding Steiner triple systems in hexagon triple systems
Discrete Mathematics, 2009 A \textit{Steiner triple} system of order \(n\) (or a triple system) is a pair \((S,T)\), where \(T\) is a collection of edge disjoint triangles, otherwise called triples, which partition the edge set \(K_n\) with vertex set \(S\). It is well known that the spectrum for Steiner triple systems is the set of all \(n \equiv 1\) or \(3 \pmod 6\) and that ...
C C Lindner +2 more
exaly +3 more sources
Examples and Counterexamples, 2022 This note is motivated by recent work by Feng et al. (2021) which studies Novák’s conjecture for Steiner Triple Systems and extends it to cyclic Steiner 2-designs, and more generally to cyclic 2-designs.
Marco Buratti, Francesca Merola
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The 3-way flower intersection problem for Steiner triple systems [PDF]
Discrete Mathematics & Theoretical Computer Science, 2020 The flower at a point x in a Steiner triple system (X; B) is the set of all triples containing x. Denote by J3F(r) the set of all integers k such that there exists a collection of three STS(2r+1) mutually intersecting in the same set of k + r triples, r ...
H. Amjadi, N. Soltankhah
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An electromagnetism-like method for the maximum set splitting problem [PDF]
Yugoslav Journal of Operations Research, 2013 In this paper, an electromagnetism-like approach (EM) for solving the maximum set splitting problem (MSSP) is applied. Hybrid approach consisting of the movement based on the attraction-repulsion mechanisms combined with the proposed scaling technique
Kratica Jozef
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Journal of Mathematics, 2023 In this article, we adapt the edge-graceful graph labeling definition into block designs and define a block design V,B with V=v and B=b as block-graceful if there exists a bijection f:B⟶1,2,…,b such that the induced mapping f+:V⟶Zv given by f+x=∑x∈AA ...
Dilara Erdemir, Emre Kolotoğlu
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An algebraic representation of Steiner triple systems of order 13
Examples and Counterexamples, 2021 In this paper we construct an incidence structure isomorphic to a Steiner triple system of order 13 by defining a set B of twentysix vectors in the 13-dimensional vector space V=GF(5)13, with the property that there exist precisely thirteen 6-subsets of ...
Marco Pavone
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Bicoloring Steiner Triple Systems [PDF]
The Electronic Journal of Combinatorics, 1999 A Steiner triple system has a bicoloring with $m$ color classes if the points are partitioned into $m$ subsets and the three points in every block are contained in exactly two of the color classes. In this paper we give necessary conditions for the existence of a bicoloring with 3 color classes and give a multiplication theorem for Steiner triple ...
Charles J. Colbourn +2 more
openaire +2 more sources
Almost all Steiner triple systems are almost resolvable
Forum of Mathematics, Sigma, 2020 We show that for any n divisible by 3, almost all order-n Steiner triple systems admit a decomposition of almost all their triples into disjoint perfect matchings (that is, almost all Steiner triple systems are almost resolvable).
Asaf Ferber, Matthew Kwan
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