On cycles in the coprime graph of integers
نویسندگان
چکیده
منابع مشابه
On cycles in the coprime graph of integers
In this paper we study cycles in the coprime graph of integers. We denote by f(n, k) the number of positive integers m ≤ n with a prime factor among the first k primes. We show that there exists a constant c such that if A ⊂ {1, 2, . . . , n} with |A| > f(n, 2) (if 6|n then f(n, 2) = 2 3 n), then the coprime graph induced by A not only contains a triangle, but also a cycle of length 2l + 1 for ...
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Abstract Let (V,E) be the coprime graph with vertex set V = {1, 2, . . . , n} and edges (i, j) ∈ E if gcd(i, j) = 1. We determine the kernels of the coprime graph and its loopless counterpart as well as so-called simple bases for them (in case such bases exist), which means that basis vectors have entries only from {−1, 0, 1}. For the loopless version knowledge about the value distribution of M...
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ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 1996
ISSN: 1077-8926
DOI: 10.37236/1323