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Extensions of Steiner Triple Systems [PDF]

open access: yesJournal of Combinatorial Designs
ABSTRACTIn 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

open access: yesAnnals of Mathematics
We 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

open access: yesDiscrete 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

On anti-Novák cycle systems

open access: yesExamples 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
doaj   +1 more source

The 3-way flower intersection problem for Steiner triple systems [PDF]

open access: yesDiscrete 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
doaj   +1 more source

An electromagnetism-like method for the maximum set splitting problem [PDF]

open access: yesYugoslav 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
doaj   +1 more source

Block-Graceful Designs

open access: yesJournal 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
doaj   +1 more source

An algebraic representation of Steiner triple systems of order 13

open access: yesExamples 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
doaj   +1 more source

Bicoloring Steiner Triple Systems [PDF]

open access: yesThe 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

open access: yesForum 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
doaj   +1 more source

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