منابع مشابه
Most Odd Degree Hyperelliptic Curves Have Only One Rational Point
Consider the smooth projective models C of curves y = f(x) with f(x) ∈ Z[x] monic and separable of degree 2g + 1. We prove that for g ≥ 3, a positive fraction of these have only one rational point, the point at infinity. We prove a lower bound on this fraction that tends to 1 as g → ∞. Finally, we show that C(Q) can be algorithmically computed for such a fraction of the curves. The method can b...
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Take a graph G, an edge subset Σ ⊆ E(G), and a set of terminals T ⊆ V (G) where |T | is even. The triple (G,Σ, T ) is called a signed graft. A T -join is odd if it contains an odd number of edges from Σ. Let ν be the maximum number of edge-disjoint odd T -joins. A signature is a set of the form Σ4δ(U) where U ⊆ V (G) and |U ∩ T | is even. Let τ be the minimum cardinality a T -cut or a signature...
متن کاملChabauty’s Method Proves That Most Odd Degree Hyperelliptic Curves Have Only One Rational Point
Consider the smooth projective models C of curves y = f(x) with f(x) ∈ Z[x] monic and separable of degree 2g + 1. We prove that for g ≥ 3, a positive fraction of these have only one rational point, the point at infinity. We prove a lower bound on this fraction that tends to 1 as g →∞. Finally, we show that C(Q) can be algorithmically computed for such a fraction of the curves, via Chabauty’s me...
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We study the class of simple graphs G for which every pair of distinct odd cycles intersect in at most one edge. We give a structural characterization of the graphs in G and prove that every G ∈ G satisfies the list-edge-coloring conjecture. When ∆(G) ≥ 4, we in fact prove a stronger result about kernel-perfect orientations in L(G) which implies that G is (m∆(G) : m)edge-choosable and ∆(G)-edge...
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We put the final piece into a puzzle first introduced by Bollobás, Erdős and Szemerédi in 1975. For arbitrary positive integers n and r we determine the largest integer ∆ = ∆(r, n), for which any r-partite graph with partite sets of size n and of maximum degree less than ∆ has an independent transversal. This value was known for all even r. Here we determine the value for odd r and find that ∆(...
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ژورنال
عنوان ژورنال: American Journal of Preventive Medicine
سال: 2017
ISSN: 0749-3797
DOI: 10.1016/j.amepre.2016.07.030