图的强制着色函数
The forced colouring function of a graph
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中文总结 AI 辅助
本文研究图的强制着色函数，确立其基本性质，给出特定点导数的组合解释，并证明在特定区间内计算其值为#P-难。
中文摘要 AI 辅助
图的强制着色函数给出了这样一个概率：对随机选择的顶点子集进行随机颜色分配后，能够通过一种称为“强制”的简单局部过程，使用相同的可用颜色集合扩展为整个图的正常着色。对于每个固定的颜色数，这是一个多项式，并且作为图多项式一般理论研究的一个课题被引入。在本文中，我们确立了其基本性质，并给出了其在两个特定点处的导数的组合解释。我们还证明了在某个区间内任意特定点处计算其值的问题是#P-难的。
英文摘要
The forced colouring function of a graph gives the probability that a random assignment of colours to a random subset of vertices can be extended, by a simple local process called forcing, to give a proper colouring of the whole graph using the same set of available colours. This is a polynomial for each fixed number of colours, and was introduced as a subject for research on the general theory of graph polynomials. In this paper we establish its fundamental properties and give combinatorial interpretations of its derivatives at two particular points. We also prove that the problem of computing its value at any specific point in a certain interval is #P-hard.
发表机构
- Monash University（莫纳什大学）
机构由 AI 辅助整理，请以论文原文为准。
