Abstract
We investigate the class of intersection graphs of paths on a grid (VPG graphs), and specifically the relationship between the bending number of a cocomparability graph and the poset dimension of its complement. We show that the bending number of a cocomparability graph G is at most the poset dimension of the complement of G minus one. Then, via Ramsey type arguments, we show our upper bound is best possible.
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Cohen, E., Golumbic, M.C., Trotter, W.T. et al. Posets and VPG Graphs. Order 33, 39–49 (2016). https://doi.org/10.1007/s11083-015-9349-9
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DOI: https://doi.org/10.1007/s11083-015-9349-9