A clique partition ε of graph G is a set of cliques such that each edge of G belongs to exactly one clique, and the total size of ε is the sum of cardinalities of all elements in ε. The ε-degree of a vertex u is the number of cliques in ε containing u. We say that ε is a k-restricted clique partition if each vertex has ε-degree at least k. The (k-restricted) clique partition number of G is the smallest cardinality of a (k-restricted) clique partition of G. In this paper, we obtain eigenvalue bounds for ε-degrees, clique partition number and restricted clique partition number of a graph. As applications, we derive the De Bruijn-Erdős Theorem from our eigenvalue bounds, obtain accurate estimation of the 2-restricted clique partition number of line graphs, and give spectral lower bounds for the minimum total size of clique partitions of a graph.

甲团划分ε图的ģ是一组派系使得每个边缘ģ属于一个集团，和的总大小ε是在所有元素的基数的总和ε。顶点u的ε度是包含u的ε中的集团数量。我们说如果每个顶点的ε度至少为k，则ε是k限制的团簇分区。G的（k限制）集团划分数是a（k-restricted）的团划分ģ。在本文中，我们获得了图的ε度，集团分割数和受限集团分割数的特征值界。作为应用程序，我们从特征值边界推导DeBruijn-Erdős定理，获得线图的2限制的集团划分数的准确估计，并给出图的集团划分的最小总大小的频谱下界。