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arXiv · 1308.4877

Posets with cover graph of pathwidth two have bounded dimension

Csaba Biró·Mitchel T. Keller·Stephen J. Young
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Abstract

Joret, Micek, Milans, Trotter, Walczak, and Wang recently asked if there exists a constant $d$ such that if $P$ is a poset with cover graph of $P$ of pathwidth at most $2$, then $\dim(P)\leq d$. We answer this question in the affirmative by showing that $d=17$ is sufficient. We also show that if $P$ is a poset containing the standard example $S_5$ as a subposet, then the cover graph of $P$ has treewidth at least $3$.

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Csaba Biró, Mitchel T. Keller, Stephen J. Young. 2015-06-03. Posets with cover graph of pathwidth two have bounded dimension. https://doi.org/10.1007/s11083-015-9359-7

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