Spanning tree congestion of [formula omitted]-outerplanar graphs

Abstract

In 1987, Simonson conjectured that every k -outerplanar graph of maximum degree d has spanning tree congestion at most k ⋅ 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 k -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.