Noncrossing Two-Nearest-Predecessor Orders on Nearly Circular Ellipses
We prove a uniform all-cardinality existence theorem for noncrossing chronological two-nearest-predecessor graphs on sufficiently near-circular ellipses. Put R = sqrt(2/sin(2*pi/5) - 1). For every ellipse with semiaxes a >= b > 0 and a/b <= R, and every finite set of at least three distinct boundary sites, there is an order starting with a triangle in which every subsequent site is joined to exactly its two Euclidean-nearest earlier sites. All edges persist, and no two independent edges properly cross. Cartesian-lexicographic order resolves equal-distance predecessor ties. The sufficient…
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