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S.B. Rao conjectured in 1971 that graphic degree sequences are well quasiordered by a relation defined in terms of the induced subgraph relation. In2008, M. Chudnovsky and P. Seymour proved this long standing Rao's Conjectureby giving structure theorems for graphic degree sequences. In this paper, weprove and use a variant of Dickson's Lemma from commutative semigroup theory togive a short proof of the bounded degree case of Rao's Conjecture that isindependent of the Chudnovsky-Seymour structure theory. In fact, weaffirmatively answer two questions of N. Robertson, the first of which impliesthe bounded degree case of Rao's Conjecture.

A Semigroup Proof of the Bounded Degree Case of S.B. Rao's Conjecture on Degree Sequences and a Bipartite Analogue