  S.B. Rao conjectured in 1971 that graphic degree sequences are well quasi
ordered by a relation defined in terms of the induced subgraph relation. In
2008, M. Chudnovsky and P. Seymour proved this long standing Rao's Conjecture
by giving structure theorems for graphic degree sequences. In this paper, we
prove and use a variant of Dickson's Lemma from commutative semigroup theory to
give a short proof of the bounded degree case of Rao's Conjecture that is
independent of the Chudnovsky-Seymour structure theory. In fact, we
affirmatively answer two questions of N. Robertson, the first of which implies
the bounded degree case of Rao's Conjecture.
