Abstract
The degenerate distance-number of a graph is the minimum number of edge lengths in a linear embedding of the graph in the plane. Carmi et al. (2008) asked whether this number is uniformly bounded for outerplanar graphs. This was resolved to the affirmative by Alon and Feldheim (2015) where they showed that nearly any three edge lengths could be used to construct a degenerate drawing for any outerplanar graph. Alon and Feldheim ask if this degenerate distance-number is in fact bounded by two. We prove this, and show that nearly every choice of two edge lengths could be used to degenerately draw all outerplanar graphs.
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