# Planar Median Graphs and Cubesquare-Graphs

@article{Seemann2021PlanarMG, title={Planar Median Graphs and Cubesquare-Graphs}, author={Carsten R. Seemann and Vincent Moulton and Peter F. Stadler and Marc Hellmuth}, journal={ArXiv}, year={2021}, volume={abs/2110.09346} }

Median graphs are connected graphs in which for all three vertices there is a unique vertex that belongs to shortest paths between each pair of these three vertices. In this paper we provide several novel characterizations of planar median graphs. More specifically, we characterize when a planar graph G is a median graph in terms of forbidden subgraphs and the structure of isometric cycles in G, and also in terms of subgraphs of G that are contained inside and outside of 4-cycles with respect…

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