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arXiv · 1301.5271

Tree-width and dimension

Gwenaël Joret·Piotr Micek·Kevin G. Milans·William T. Trotter·Bartosz Walczak·Ruidong Wang
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Abstract

Over the last 30 years, researchers have investigated connections between dimension for posets and planarity for graphs. Here we extend this line of research to the structural graph theory parameter tree-width by proving that the dimension of a finite poset is bounded in terms of its height and the tree-width of its cover graph.

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Gwenaël Joret, Piotr Micek, Kevin G. Milans, William T. Trotter, Bartosz Walczak, Ruidong Wang. 2015-02-25. Tree-width and dimension. https://doi.org/10.1007/s00493-014-3081-8

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