Date of Original Version

1-13-2013

Type

Article

Rights Management

copyright © by International Press of Boston

Abstract or Description

We consider the endpoint sets produced by Pósa rotations, when applied to a longest path in a random graph with cn edges, conditioned on having minimum degree at least three. We prove that, for c≥2.7, the Pósa sets are likely to be almost linear in n, implying that the number of missing edges, each allowing either to get a longer path or to form a Hamilton cycle, is almost quadratic in n.

DOI

10.4310/JOC.2013.v4.n2.a1

Included in

Mathematics Commons

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Published In

Journal of Combinitorics, 4, 2, 123-156.