A graph transformation called the compression of a graph G is known to decrease the number of spanning trees, the all-terminal reliability, and the magnitude of the coefficients of the chromatic polynomial of a graph G. All of these graph parameters can be derived from the Tutte polynomial of G, and in this paper we determine more generally compression's effect on the Tutte polynomial, recovering the previous results and obtaining similar results for a wide variety of other graph parameters derived from the Tutte polynomial. Since any simple connected graph can be transformed into a connected threshold graph via a series of compressions, this gives that threshold graphs are extremal simple graphs for all of the parameters considered.

已知称为图G压缩的图变换可以减少生成树的数量、全终端可靠性以及图G的色多项式系数的大小。所有这些图形参数都可以从G的 Tutte 多项式导出，在本文中，我们更一般地确定压缩对 Tutte 多项式的影响，恢复以前的结果，并为从 Tutte 导出的各种其他图形参数获得类似的结果多项式。由于任何简单的连通图都可以通过一系列压缩转换为连通阈值图，这使得阈值图是所有考虑参数的极值简单图。