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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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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
Colouring of cubic graphs by Steiner triple systems
 JOURNAL OF COMBINATORIAL THEORY, SERIES B
, 2004
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Characterisation results for Steiner triple systems and their application to edgecolourings of cubic graphs
, 2010
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Equitable edge colored Steiner triple systems
 AUSTRALASIAN JOURNAL OF COMBINATORICS VOLUME 50 (2011), PAGES 155–163
, 2011
"... A kedge coloring of G is said to be equitable if the number of edges, at any vertex, colored with a certain color differ by at most one from the number of edges colored with a different color at the same vertex. An STS(v) is said to be polychromatic if the edges in each triple are colored with thre ..."
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A kedge coloring of G is said to be equitable if the number of edges, at any vertex, colored with a certain color differ by at most one from the number of edges colored with a different color at the same vertex. An STS(v) is said to be polychromatic if the edges in each triple are colored
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.
unknown title
"... We develop an idea of a local 3edgecoloring of a cubic graph, a generalization of the usual 3edgecoloring. We allow for an unlimited number of colors but require that the colors of two edges meeting at a vertex always determine the same third color. Local 3edgecolorings are described in terms ..."
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of colorings by points of a partial Steiner triple system such that the colors meeting at each vertex form a triple of the system. An important place in our investigation is held by the two smallest nontrivial Steiner triple systems, the Fano plane PG(2, 2) and the affine plane AG(2, 3). For i = 4, 5, and 6
Ideals, varieties, stability, colorings and combinatorial designs
"... A combinatorial design is equivalent to a stable set in a suitably chosen Johnson graph, whose vertices correspond to all ksets that could be blocks of the design. In order to find maximum stable sets of a graph G, two ideals are associated with G, one constructed from the MotzkinStrauss formula a ..."
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graphs provide an algebraic characterization that can be used to generate Steiner triple systems. Two different ideals for the generation of Steiner triple systems, and a third for Kirkman triple systems, are developed. The last of these combines stability and colorings. 1
The Many Names of (7, 3, 1)
, 2002
"... In the world of discrete mathematics, we encounter a bewildering variety of topics with no apparent connection between them. But appearances are deceptive. For example, combinatorics tells us about difference sets, block designs, and triple systems. Geometry leads us to finite projective planes and ..."
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. Finally, in these fields we encounter such names as Euler, Fano, Fischer, Hadamard, Heawood, Kirkman, Singer and Steiner. This is a story about a single object that connects all of these. Commonly known as (7, 3, 1), it is all at once a difference set, a block design, a Steiner triple system, a finite
On symmetric subgraphs of the 7cube: an overview
 Discrete Math
, 1994
"... It is shown that the graph QQ) C obtained from the 7cube QQ) by deletion of a perfect Hamming code C has a spanning selfcomplementary subgraph which is edgetransitive but not vertextransitive and also extremal among all the cube subgraphs which are squareblocking and codeavoiding. Our work uses ..."
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uses combinatorial techniques involving orientations on the Fano plane and the resulting Steiner triple systems. In this paper, we study some combinatorial properties of a cubic bipartite graph, that we will denote by W, which is edgetransitive but not vertextransitive. Bouwer mentioned at the end
Results 1  10
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13