Spanning tree congestion of kk-outerplanar graphs

In 1987, Simonson conjectured that every kk-outerplanar graph of maximum degree dd has spanning tree congestion at most k⋅dk⋅d [S. Simonson, A variation on the min cut linear arrangement problem, Math. Syst. Theory 20 (1987) 235–252]. We show that his conjecture is true and the bound is tight for outerplanar graphs and kk-outerplanar graphs of maximum degree 4. We give a precise characterization of the spanning tree congestion of outerplanar graphs, and thus show that the spanning tree congestion of outerplanar graphs can be determined in linear time.