一种最一般的边消除多项式--边的加厚
A Most General Edge Elimination Polynomial - Thickening of Edges
摘要：
我们考虑一个由Averbouch，Godlin，and Makowsky（2007）引入的图多项式<$（G;x，y，z）。该图多项式同时推广了Tutte多项式以及Dohmen，Poenitz和Tittmann（2003）定义的二元色多项式。我们推导出一个恒等式，它将一个厚图（即一个图的每条边都被它的k个副本所取代）的图多项式与原始图的图多项式联系起来。因此，我们观察到在每个点（x，y，z），除了位于某个2维集合内的点，计算是#P-hard的。
英文摘要：
We consider a graph polynomial ξ(G;x,y,z) introduced by Averbouch, Godlin, and Makowsky (2007). This graph polynomial simultaneously generalizes the Tutte polynomial as well as a bivariate chromatic polynomial defined by Dohmen, Poenitz and Tittmann (2003). We derive an identity which relates the graph polynomial of a thicked graph (i.e. a graph with each edge replaced by k copies of it) to the graph polynomial of the original graph. As a consequence, we observe that at every point (x,y,z), except for points lying within some set of dimension 2, evaluating ξis #P-hard.
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