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, Volume 28, Issue 3, pp 455–464 | Cite as

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

  • Gwenaël Joret
  • Kevin G. Milans
Article

Abstract

A poset is \((\underline{r}+\underline{s})\)-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 \((\underline{r}+\underline{s})\)-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 et al. (SIAM J Discrete Math 23(4):1992–1999, 2010).

Keywords

First-Fit On-line chain partition Column construction method Forbidden subposet 

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Copyright information

© Springer Science+Business Media B.V. 2010

Authors and Affiliations

  1. 1.Département d’InformatiqueUniversité Libre de BruxellesBrusselsBelgium
  2. 2.Department of MathematicsUniversity of South CarolinaColumbiaUSA

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