We show that any loopy multigraph with a graphical degree sequence can be transformed into a simple graph by a finite sequence of double edge swaps with each swap involving at least one loop or multiple edge. Our result answers a question of Janson motivated by random graph theory, and it adds to the rich literature on reachability of double edge swaps with applications in Markov chain Monte Carlo sampling from the uniform distribution of graphs with prescribed degrees.

中文翻译：

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通过一系列双边交换使多图变得简单

我们表明，具有图形化程度序列的任何循环多图都可以通过双边交换的有限序列转换为简单图，每次交换至少涉及一个循环或多边。我们的结果回答了由随机图论激发的Janson问题，它为双边互换的可及性提供了丰富的文献，并从具有指定度的图的均匀分布中将其应用于马尔可夫链蒙特卡洛采样。