Colouring Steiner systems with specified block colour patterns
نویسندگان
چکیده
منابع مشابه
On some colouring of 4-cycle systems with specified block colour patterns
The present paper continues the study (begun by Quattrocchi, Colouring 4-cycle systems with specified block colour pattern: the case of embedding P3-designs, Electron. J. Combin., 8 (2001)) of 4-cycle systems with specified block colour patterns that are also strict colourings in the sense of Voloshin (Coloring Mixed Hypergraphs: Theory, Algorithms and Applications, American Mathematical Societ...
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A colouring of a 4-cycle system (V,B) is a surjective mapping φ : V → Γ. The elements of Γ are colours. If |Γ| = m, we have an m-colouring of (V,B). For every B ∈ B, let φ(B) = {φ(x)|x ∈ B}. There are seven distinct colouring patterns in which a 4-cycle can be coloured: type a (××××, monochromatic), type b (×××2, two-coloured of pattern 3 + 1), type c (× × 22, two-coloured of pattern 2 + 2), ty...
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Hill [6] showed that the largest cap in PG(5, 3) has cardinality 56. Using this cap it is easy to construct a cap of cardinality 45 in AG(5, 3). Here we show that the size of a cap in AG(5, 3) is bounded above by 48. We also give an example of three disjoint 45-caps in AG(5, 3). Using these two results we are able to prove that the Steiner triple system AG(5, 3) is 6-chromatic, and so we exhibi...
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Let S be a Steiner triple system and G a cubic graph. We say that G is S-colourable if its edges can be coloured so that at each vertex the incident colours form a triple of S. We show that if S is a projective system PG(n, 2), n ≥ 2, then G is S-colourable if and only if it is bridgeless, and that every bridgeless cubic graph has an S-colouring for every Steiner triple system of order greater ...
متن کاملColouring Cubic Graphs by Small Steiner Triple Systems
Given a Steiner triple system S, we say that a cubic graph G is S-colourable 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 that every simple cubic graph is U-colourable. This improves the result of Grannell et al. [J. Gr...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2001
ISSN: 0012-365X
DOI: 10.1016/s0012-365x(00)00388-5