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arXiv · 1006.5704

First-Fit is Linear on Posets Excluding Two Long Incomparable Chains

Gwenaël Joret·Kevin G. Milans
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Abstract

A poset is (r + s)-free if it does not contain two incomparable chains of size r and s, respectively. We prove that when r and s are at least 2, the First-Fit algorithm partitions every (r + s)-free poset P into at most 8(r-1)(s-1)w chains, where w is the width of P. This solves an open problem of Bosek, Krawczyk, and Szczypka (SIAM J. Discrete Math., 23(4):1992--1999, 2010).

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Gwenaël Joret, Kevin G. Milans. 2010-10-08. First-Fit is Linear on Posets Excluding Two Long Incomparable Chains. https://doi.org/10.1007/s11083-010-9184-y

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