AI 中文总结
该研究提出基于图论操作的多项式时间算法，核心是通过迭代计算加权路径判定完美图是否含给定大小团，权重先统一初始化再依上次迭代路径计数更新，用于对完美图进行最优着色。
AI 中文摘要
我们提出了一种完全基于图论操作的多项式时间算法，用于对完美图进行最优着色。该算法核心是通过迭代计算图中边和非边赋予特定权重的路径，来判定完美图是否包含给定大小的团。权重按统一方案初始化，然后在每次迭代中根据上一次迭代的路径计数进行更新。
英文摘要
We present a polynomial-time algorithm for optimally coloring perfect graphs that is based entirely on graph-theoretic operations. At its core, the algorithm decides whether a perfect graph contains a clique of a given size by iteratively counting walks in the graph with certain weights assigned to its edges and nonedges. These weights are initialized according to a uniform scheme and then updated in each iteration based on the walk counts from the previous iteration.
