首页/论文/2004.02162

arXiv 2004.021622020-04-05math.CO

Dilworth's Theorem for Borel Posets

Bartłomiej Bosek, Jarosław Grytczuk, Zbigniew Lonc

英文摘要：

A famous theorem of Dilworth asserts that any finite poset of width $k$ can be decomposed into $k$ chains. We study the following problem: given a Borel poset $P$ of finite width $k$, is it true that it can be decomposed into $k$ Borel chains? We give a positive answer in a special case of Borel posets embeddable into the real line. We also prove a dual theorem for posets whose comparability graphs are locally countable.

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