Karp–Sipser on Random Graphs with a Fixed Degree Sequence
2011 ◽
Vol 20
(5)
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pp. 721-741
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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 n ∥ z ∥ 1/2 − o(n1−ε) edges in Gz, where ε = ε (Δ, z) is a constant.
2010 ◽
Vol 24
(2)
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pp. 558-569
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2012 ◽
Vol 41
(2)
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pp. 179-214
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2007 ◽
Vol 16
(05)
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pp. 733
◽
2008 ◽
Vol 17
(1)
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pp. 67-86
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Keyword(s):
2011 ◽
Vol 21
(4)
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pp. 1400-1435
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Keyword(s):
2009 ◽
Vol 18
(5)
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pp. 775-801
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