منابع مشابه
Perfect divisibility and 2-divisibility
A graph G is said to be 2-divisible if for all (nonempty) induced subgraphs H of G, V (H) can be partitioned into two sets A,B such that ω(A) < ω(H) and ω(B) < ω(H). A graph G is said to be perfectly divisible if for all induced subgraphs H of G, V (H) can be partitioned into two sets A,B such that H[A] is perfect and ω(B) < ω(H). We prove that if a graph is (P5, C5)-free, then it is 2-divisibl...
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For given integers a, b and j ≥ 1 we determine the set R (j) a,b of integers n for which a n − b is divisible by n . For j = 1, 2, this set is usually infinite; we determine explicitly the exceptional cases for which a, b the set R (j) a,b (j = 1, 2) is finite. For j = 2, we use Zsigmondy’s Theorem for this. For j ≥ 3 and gcd(a, b) = 1, R (j) a,b is probably always finite; this seems difficult ...
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ژورنال
عنوان ژورنال: Nature
سال: 1897
ISSN: 0028-0836,1476-4687
DOI: 10.1038/057054a0