简单（2，2）-稀疏拟阵回路的构造性刻画
A Constructive Characterisation of Circuits in the Simple (2,2)-sparsity Matroid
摘要：
我们提供了一个简单的（2，2）-稀疏拟阵电路的建设性特征。一个电路是一个单图G=（V，E），其中|E| =2 |V|-1，且由任何$X \subsetneq V$诱导的边数至多为2 |X|-2.坚持简单性导致Henneberg运算只有在图充分连通时才是足够的。因此，我们引入3种不同的连接操作来完成特征化。扩展时的稀疏拟阵是连接的，这是适用于理论的框架表面上提供一个固定的表征时，框架上的一个无限的圆柱是一般的全球刚性。
英文摘要：
We provide a constructive characterisation of circuits in the simple (2,2)-sparsity matroid. A circuit is a simple graph G=(V,E) with |E|=2|V|-1 and the number of edges induced by any $X \subsetneq V$ is at most 2|X|-2. Insisting on simplicity results in the Henneberg operation being enough only when the graph is sufficiently connected. Thus we introduce 3 different join operations to complete the characterisation. Extensions are discussed to when the sparsity matroid is connected and this is applied to the theory of frameworks on surfaces to provide a conjectured characterisation of when frameworks on an infinite circular cylinder are generically globally rigid.
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