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A census of the orientable biembeddings of Steiner triple systems of order 15
"... A complete census is given of the orientable biembeddings of Steiner triple systems of order 15. There are 80 Steiner triple systems of order 15 and these generate a total of 9 530 orientable biembeddings. 1 ..."
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A complete census is given of the orientable biembeddings of Steiner triple systems of order 15. There are 80 Steiner triple systems of order 15 and these generate a total of 9 530 orientable biembeddings. 1
Nonorientable biembeddings of Steiner triple systems
 DISCRETE MATHEMATICS
, 2004
"... Constructions due to Ringel show that there exists a nonorientable face 2colourable triangular embedding of the complete graph on n vertices (equivalently a nonorientable biembedding of two Steiner triple systems of order n) for all n ≡ 3 (mod 6) with n ≥ 9. We prove the corresponding existence th ..."
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Constructions due to Ringel show that there exists a nonorientable face 2colourable triangular embedding of the complete graph on n vertices (equivalently a nonorientable biembedding of two Steiner triple systems of order n) for all n ≡ 3 (mod 6) with n ≥ 9. We prove the corresponding existence
Orientable biembeddings of cyclic Steiner triple systems from current assignments on Möbius Ladder Graphs
, 2008
"... We give a characterization of a current assignment on the bipartite Möbius ladder graph with 2n + 1 rungs. Such an assignment yields an index one current graph with current group Z12n+7 that generates an orientable face 2colorable triangular embedding of the complete graph K12n+7 or, equivalentl ..."
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, equivalently, an orientable biembedding of two cyclic Steiner triple systems of order 12n+7. We use our characterization to construct Skolem sequences that give rise to such current assignments. These produce many nonisomorphic orientable biembeddings of cyclic Steiner triple systems of order 12n + 7.
Orientable selfembeddings of Steiner triple systems of order 15
 ACTA MATH. UNIV. COMENIANAE
"... It is shown that for 78 of the 80 isomorphism classes of Steiner triple systems of order 15 it is possible to find a face 2colourable triangulation of the complete graphK15 in an orientable surface in which the colour classes both form representatives of the specified isomorphism class. For one o ..."
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It is shown that for 78 of the 80 isomorphism classes of Steiner triple systems of order 15 it is possible to find a face 2colourable triangulation of the complete graphK15 in an orientable surface in which the colour classes both form representatives of the specified isomorphism class. For one
On 2ranks of Steiner triple systems
 Electron. J. Combin., 2:Research Paper
, 1995
"... Introduction The work we report on here began as an effort to understand the surprising facts uncovered by a comprehensive computer study of the 80 Steiner triple systems of order 6 (on 15 points) undertaken by Tonchev and Weishaar [21]. Among the results we establish, perhaps the easiest to state ..."
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Introduction The work we report on here began as an effort to understand the surprising facts uncovered by a comprehensive computer study of the 80 Steiner triple systems of order 6 (on 15 points) undertaken by Tonchev and Weishaar [21]. Among the results we establish, perhaps the easiest to state
A Census Of Steiner Triple Systems And Some Related Combinatorial Objects
, 2003
"... A Steiner triple system of order v (STS(v)) is a set of triples, or blocks, constructed over a set of v points, such that every pair of distinct points occurs in a unique block. Previously, ..."
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A Steiner triple system of order v (STS(v)) is a set of triples, or blocks, constructed over a set of v points, such that every pair of distinct points occurs in a unique block. Previously,
The Steiner Quadruple Systems of Order 16
"... The Steiner quadruple systems of order 16 are classified up to isomorphism by means of an exhaustive computer search. The number of isomorphism classes of such designs is 1,054,163. Properties of the designs—including the orders of the automorphism groups and the structures of the derived Steiner t ..."
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triple systems of order 15—are tabulated. A doublecounting consistency check is carried out to gain confidence in the correctness of the classification.
Minimum embedding of Steiner triple systems into (K4
 e)designs, Discrete Math
"... A (K4−e)design on v+w points embeds a Steiner triple system if there is a subset of v points on which the graphs of the design induce the blocks of a Steiner triple system. It has been established that w ≥ v/3, and that when equality is met, such a minimum embedding of an STS(v) exists, except when ..."
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A (K4−e)design on v+w points embeds a Steiner triple system if there is a subset of v points on which the graphs of the design induce the blocks of a Steiner triple system. It has been established that w ≥ v/3, and that when equality is met, such a minimum embedding of an STS(v) exists, except
Colouring cubic graphs by small Steiner triple systems
"... Given a Steiner triple system S, we say that a cubic graph G is Scolourable if its edges can be coloured by points of S in such way that the colours of any three edges meeting at a vertex form a triple of S. We prove that there is Steiner triple system U of order 21 which is universal in the sense ..."
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that every simple cubic graph is Ucolourable. This improves the result of Grannell et al. [J. Graph Theory 46 (2004), 15–24] who found a similar system of order 381. On the other hand, it is known that any universal Steiner triple system must have order at least 13, and it has been conjectured
WellOrdered Steiner Triple Systems and 1Perfect Partitions of the NCube
, 1999
"... Binary 1perfect codes which give rise to partitions of the ncube are presented. The 1perfect partitions are characterized as homomorphic images of simple algebraic structures on F n and are constructed starting from a particular case of a structure defined in F n. A special property (socalled w ..."
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called wellordering) ofSTS(n) is given in such a way that for this kind of STS it is possible to define the algebraic structure we need in F n and to construct 1perfect partitions of the ncube. These 1perfect partitions give us a kind of 1perfect code for which it is easy to do the coding and decoding
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