  To solve Nagata's conjecture, Shestakov-Umirbaev constructed a theory for
deciding wildness of polynomial automorphisms in three variables. Recently,
Kara\'s and others study multidegrees of polynomial automorphisms as an
application of this theory. They give various necessary conditions for triples
of positive integers to be multidegrees of tame automorphisms in three
variables. In this paper, we prove a strong theorem unifying these results
using the generalized Shestakov-Umirbaev theory.
