Constant 2-labellings and an application to (r,a,b)-covering codes
نویسندگان
چکیده
منابع مشابه
Constant 2-labellings and an application to (r, a, b)-covering codes
We introduce the concept of constant 2-labelling of a vertex-weighted graph and show how it can be used to obtain perfect weighted coverings. Roughly speaking, a constant 2-labelling of a vertex-weighted graph is a black and white colouring of its vertex set which preserves the sum of the weights of black vertices under some automorphisms. We study constant 2-labellings on four types of vertex-...
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A sequence (ai) of integers is well-spread if the sums ai +a j, for i < j, are all different. For a fixed positive integer r, let Wr(N) denote the maximum integer n for which there exists a well-spread sequence 0≤ a1 < · · ·< an ≤ N with ai ≡ a j (mod r) for all i, j. We give a new proof that Wr(N) < (N/r)1/2 + O((N/r)1/4); our approach improves a bound of Ruzsa [Acta. Arith. 65 (1993), 259–283...
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ژورنال
عنوان ژورنال: Discussiones Mathematicae Graph Theory
سال: 2017
ISSN: 1234-3099,2083-5892
DOI: 10.7151/dmgt.1973