匹配测度的原子
Atoms of the matching measure
摘要：
证明了点传递连通图的匹配测度不含原子。推广Salez的结果，我们证明了对于度一致有界的遍历非顺从单模随机有根图，匹配测度只有200个原子。Ku和Chen证明了有限图匹配多项式的非零根的Gallai-Edmonds结构定理的类似定理。我们将他们的结果推广到无限图。我们还表明，相应的Gallai-Edmonds分解是兼容的零温度单体-二聚体模型。
英文摘要：
We prove that the matching measure of an infinite vertex-transitive connected graph has no atoms. Generalizing the results of Salez, we show that for an ergodic non-amenable unimodular random rooted graph with uniformly bounded degrees, the matching measure has only finitely many atoms. Ku and Chen proved the analogue of the Gallai-Edmonds structure theorem for non-zero roots of the matching polynomial for finite graphs. We extend their results for infinite graphs. We also show that the corresponding Gallai-Edmonds decomposition is compatible with the zero temperature monomer-dimer model.
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