2019/08/13 by Felsner, Stefan · 1 citation
#68R10 (primary) 06A07 (secondary) #Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.1908.04524
We show that 4-connected plane triangulations can be redrawn such that edges are represented by straight segments and the vertices are covered by a set of at most √(2n) lines each of them horizontal or vertical. The same holds for all subgraphs of such triangulations. The proof is based on a corresponding result for diagrams of planar lattices which makes use of orthogonal chain and antichain families.