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A note on the abc conjecture

✍ Scribed by Pei-Chu Hu; Chung-Chun Yang


Publisher
John Wiley and Sons
Year
2002
Tongue
English
Weight
187 KB
Volume
55
Category
Article
ISSN
0010-3640

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We show that there exists an infinite sequence of sums P: a+b=c of rational integers with large height compared to the radical: h(P) r(P)+4K l -h(P)Γ‚log h(P) with K l =2 lΓ‚2 4 -2?Γ‚e>1.517 for l=0.5990. This improves the result of Stewart and Tijdeman [9]. The value of l comes from an asymptotic boun

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## Abstract In 1978 Woodall [6] conjectured the following: in a planar digraph the size of a shortest cycle is equal to the maximum cardinality of a collection of disjoint tranversals of cycles. We prove that this conjecture is true when the digraph is series‐parallel. In fact, we prove a stronger

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A graph H is a cover of a graph G, if there exists a mapping Ο• from V (H) onto V (G) such that for every vertex v of G, Ο• maps the neighbors of v in H bijectively onto the neighbors of Ο•(v) in G. Negami conjectured in 1987 that a connected graph has a finite planar cover if and only if it embeds in

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