On some colouring of 4-cycle systems with specified block colour patterns
نویسندگان
چکیده
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 Society, Providence R.I. (2002)). Here we consider colourings with patterns of size 3 or 4 such that each colour class C induces a P2-design embedded into the 4-cycle system. AMS classification: 05B05.
منابع مشابه
Colouring 4 - cycle systems with specified block colour patterns : the case of embedding P 3 - designs ∗ Gaetano
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...
متن کاملEquitable 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...
متن کاملEquitable Block Colourings for Systems of 4-Kites
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...
متن کاملColouring 4-cycle systems with equitably coloured blocks
A colouring of a 4-cycle system (V,B) is a surjective mapping φ : V → Γ. The elements of Γ are colours and, for each i ∈ Γ, the set Ci = φ−1(i) is a colour class. If |Γ| = m, we have an m-colouring of (V,B). For every B ∈ B, let φ(B) = {φ(x) | x ∈ B}. We say that a block B is equitably coloured if either |φ(B)∩Ci| = 0 or |φ(B)∩Ci| = 2 for every i ∈ Γ. Let F(n) be the set of integersm such that ...
متن کاملبررسی اثر آنزیم آلفا آمیلاز بر کیفیت ماکارونی
Macaroni is a food product generally considered as one of the paste products. These products are produced from semolina that is, in turn, produced through special processing of milled durum wheat. In order to examine the effect of α-amylase on macaroni quality, three cultivars, namely Yavarous, Zardak and Altar 84, were chosen from each of which some wheat sprouts were prepared and mixed with...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Discrete Mathematics
دوره 308 شماره
صفحات -
تاریخ انتشار 2008