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On 6-sparse Steiner triple systems
Journal of Combinatorial Theory - Series A, 2007 A Steiner triple system of order \(v\) \([\text{STS}(v)]\) consists of a \(v\)-set \(V\) of elements and a family \(B\) of 3-subsets of \(V\) called triples such that each 2-subset of \(V\) is contained in exactly one triple of \(B\). A configuration in an \(\text{STS}(v)\) is a partial triple system consisting typically of a small number of triples ...
T S Griggs
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Dominating Set for Bipartite Graph Γ(v, k, l, 2) [PDF]
Mathematics Interdisciplinary Research, 2023 A bipartite graph (X, Y ) in which X and Y are, respectively, the set ofall l-subsets and all k-subsets of a v-set V as vertices and two vertices beingadjacent if they have i elements in common, is denoted by Γ(v, k, l, i).
Abolfazl Bahmani +2 more
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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 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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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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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
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Total dominator chromatic number of Kneser graphs
AKCE International Journal of Graphs and Combinatorics, 2023 Decomposition into special substructures inheriting significant properties is an important method for the investigation of some mathematical structures. A total dominator coloring (briefly, a TDC) of a graph G is a proper coloring (i.e.
Parvin Jalilolghadr, Ali Behtoei
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Enumerating Steiner triple systems
Journal of Combinatorial Designs, 2023 AbstractSteiner triple systems (STSs) have been classified up to order 19. Earlier estimations of the number of isomorphism classes of STSs of order 21, the smallest open case, are discouraging as for classification, so it is natural to focus on the easier problem of merely counting the isomorphism classes.
Östergård +2 more
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Hypergraphs with infinitely many extremal constructions
Discrete Analysis, 2023 Hypergraphs with infinitely many extremal constructions, Discrete Analysis 2023:18, 34 pp. A fundamental result in extremal graph theory, Turán's theorem, states that the maximal number of edges of a graph with $n$ vertices that does not contain a ...
Jianfeng Hou +4 more
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