S.B.有界度情形的半群证明Rao关于度序列的猜想和一个二分映射
A Semigroup Proof of the Bounded Degree Case of S.B. Rao's Conjecture on Degree Sequences and a Bipartite Analogue
摘要：
S.B. Rao在1971年证明了图的度序列是由一个由诱导子图关系定义的关系很好地拟序的。2008年，M. Chudnovsky和P. Seymour通过给出图度序列的结构定理证明了这个长期存在的Rao猜想。本文证明并利用交换半群理论中Dickson引理的一个变形，给出了Rao猜想的有界度情形的一个简短证明，它与Chudnovsky-Seymour结构理论无关.事实上，我们肯定地回答了N的两个问题。Robertson，其中第一个暗示了Rao猜想的有界度情况。
英文摘要：
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.
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