Tree-width and dimension

@article{Joret2016TreewidthAD,
  title={Tree-width and dimension},
  author={Gwena{\"e}l Joret and Piotr Micek and Kevin G. Milans and W. Trotter and B. Walczak and R. Wang},
  journal={Combinatorica},
  year={2016},
  volume={36},
  pages={431-450}
}
  • Gwenaël Joret, Piotr Micek, +3 authors R. Wang
  • Published 2016
  • Computer Science, Mathematics
  • Combinatorica
  • 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. 

    Figures and Topics from this paper.

    Explore Further: Topics Discussed in This Paper

    Planar Posets Have Dimension at Most Linear in Their Height
    9
    On the Dimension of Posets with Cover Graphs of Treewidth 2
    22
    Minors and dimension
    18
    Posets with Cover Graph of Pathwidth two have Bounded Dimension
    15
    Boolean dimension and local dimension
    8
    Sparsity and dimension
    2
    Sparsity and Dimension
    15
    Dimension and cut vertices: an application of Ramsey theory
    9

    References

    Publications referenced by this paper.
    SHOWING 1-10 OF 70 REFERENCES
    Diameter and Treewidth in Minor-Closed Graph Families
    278
    Bipartite Graphs, Upward Drawings, and Planarity
    52
    Minors and dimension
    18
    Dimension and height for posets with planar cover graphs
    21
    The dimension of planar posets
    60
    Complexity of diagrams
    13