Block colourings of 6-cycle systems
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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An edge colouring of a graph is said to be an r-local colouring if the edges incident to any vertex are coloured with at most r colours. Generalising a result of Bessy and Thomassé, we prove that the vertex set of any 2-locally coloured complete graph may be partitioned into two disjoint monochromatic cycles of different colours. Moreover, for any natural number r, we show that the vertex set o...
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In 1992 Gyárfás showed that a graph G having only k odd cycle lengths is (2k + 1)colourable, if it does not contain a K2k+2. In this paper, we will present the results for graphs containing only odd cycles of length 2m − 1 and 2m + 1 as done in [S. Matos Camacho, Colourings of graph with prescribed cycle lengths, diploma thesis, TU Bergakademie Freiberg, 2006. [3]]. We will show that these grap...
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ژورنال
عنوان ژورنال: Opuscula Mathematica
سال: 2017
ISSN: 1232-9274
DOI: 10.7494/opmath.2017.37.5.647