Equitable specialized block-colourings for 4-cycle systems — II
نویسندگان
چکیده
منابع مشابه
Equitable block colourings for 8-cycle systems
Let Σ = (X,B) be an 8-cycle system of order v = 1+16k. A c-colouring of type s is a map φ : B → C, with C set of colours, so that exactly c colours are used and for every vertex x all the blocks containing x are coloured with exactly s colours. Let 8k = qs+ r, with q, r ≥ 0. The colouring φ is called equitable if for every vertex x the set of the 8k blocks containing x is partitioned into r col...
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An equitable colouring of a balanced G-design (X,B) is a map φ∶B → C such that ∣bi(x) − bj(x)∣ ≤ 1 for any x ∈ X and i, j, with i ≠ j, being bi(x) the number of blocks containing the vertex x and coloured with the colour i. A c-colouring is a colouring in which exactly c colours are used. A c-colouring of type s is a colourings in which, for every vertex x, all the blocks containing x are colou...
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Let Σ = (X,B) a 4-cycle system of order v = 1 + 8k. A c-colouring of type s is a map φ∶B → C, with C set of colours, such that exactly c colours are used and for every vertex x all the blocks containing x are coloured exactly with s colours. Let 4k = qs + r, with q, r ≥ 0. φ is equitable if for every vertex x the set of the 4k blocks containing x is parted in r colour classes of cardinality q +...
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In this paper, we give necessary and sufficient conditions for the existence of equitable partial 4-cycle and 5-cycle systems. Furthermore, we construct equitable partial 4-cycle and 6-cycle systems of Kn,n'
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There is a vast literature already in existence on colourings in graphs and designs. We refer the interested reader to [2, 7, 8, 11, 12]. A major application of such colourings is to sampling and scheduling problems. For an excellent consideration of designs for statistical purposes, see [13]; in [8], examples of graph colouring applications in scheduling are described. Let P be a point set and...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2010
ISSN: 0012-365X
DOI: 10.1016/j.disc.2010.03.018