First-Fit is Linear on Posets Excluding Two Long Incomparable Chains
Combinatorics
2011-11-11 v3
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).
Cite
@article{arxiv.1006.5704,
title = {First-Fit is Linear on Posets Excluding Two Long Incomparable Chains},
author = {Gwenaël Joret and Kevin G. Milans},
journal= {arXiv preprint arXiv:1006.5704},
year = {2011}
}
Comments
v3: fixed some typos