论文标题
匹配度量的原子
Atoms of the matching measure
论文作者
论文摘要
我们证明，无限顶点连接图的匹配度量没有原子。概括了Salez的结果，我们表明，对于具有均匀界限度的梯形的非无型随机根系图，匹配度量只有有限的许多原子。 KU和Chen证明了Gallai-Edmonds结构定理的类似于有限图的匹配多项式的非零根。我们扩展了无限图的结果。我们还表明，相应的加莱 - 埃德蒙兹分解与零温度单体二聚体模型兼容。
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.
