Clin dʹoeil on L1-embeddable planar graphs Original Research Article

In this note we present some properties of L1-embeddable planar graphs. We present a characterization of graphs isometrically embeddable into half-cubes. This result implies that every planar L1-graph G has a scale 2 embedding into a hypercube. Further, under some additional conditions we show that for a simple circuit C of a planar L1-graph G the subgraph H of G bounded by C is also L1-embeddable. In many important cases, the length of C is the dimension of the smallest cube in which H has a scale embedding. Using these facts we establish the L1-embeddability of a list of planar graphs.