On the bend-number of planar and outerplanar graphs

The bend-number  b(G)b(G) of a graph GG is the minimum kk such that GG may be represented as the edge intersection graph of a set of grid paths with at most kk bends. We confirm a conjecture of Biedl and Stern showing that the maximum bend-number of outerplanar graphs is 2. Moreover we improve the formerly known lower and upper bounds for the maximum bend-number of planar graphs from 2 and 5 to 3 and 4, respectively.