Date of Original Version

5-16-2011

Type

Article

Rights Management

© Cambridge University Press

Abstract or Description

Let Δ ≥ 3 be an integer. Given a fixed z+Δ such that zΔ > 0, we consider a graph Gz drawn uniformly at random from the collection of graphs with zin vertices of degree i for i = 1,. . .,Δ. We study the performance of the Karp–Sipser algorithm when applied to Gz. If there is an index δ > 1 such that z1 = . . . = zδ−1 = 0 and δzδ,. . .,ΔzΔ is a log-concave sequence of positive reals, then with high probability the Karp–Sipser algorithm succeeds in finding a matching with nz1/2 − o(n1−ε) edges in Gz, where ε = ε (Δ, z) is a constant.

DOI

10.1017/S0963548311000265

Included in

Mathematics Commons

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Published In

Combinatorics, Probability and Computing, 20, 5, 721-741.