Tree-width and dimension

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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Corresponding author

Correspondence to William T. Trotter.

Additional information

Bartosz Walczak was supported by Polish National Science Center grant 2011/03/N/ST6/03111.

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Joret, G., Micek, P., Milans, K.G. et al. Tree-width and dimension. Combinatorica 36, 431–450 (2016). https://doi.org/10.1007/s00493-014-3081-8

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Keywords

  • Planar Graph
  • Linear Order
  • Discrete Math
  • Minimal Element
  • Linear Extension