标题： 关于端点具有等度的路径的 Erdős-Hajnal 问题的补遗 显示英文标题

标题： A complement of the Erdős-Hajnal problem on paths with equal-degree endpoints

摘要： 回答 Erdős 和 Hajnal 的一个问题，Chen 和 Ma 证明了对于所有的$n\geq600$，具有$2n + 1$个顶点和至少$n^2 + n+1$条边的图中包含两个度数相等的顶点，并且这两个顶点由一条长度为三的路径连接，而完全二分图$K_{n,n+1}$表明这个边界的限制是尖锐的。 在本文中，我们得到了对于所有$n\ge2$的上述结果，从而完全解决了 Erdős 和 Hajnal 的问题。 显示英文摘要

摘要： Answering a question of Erd\H{o}s and Hajnal, Chen and Ma proved that for all $n\geq600$ every graph with $2n + 1$ vertices and at least $n^2 + n+1$ edges contains two vertices of equal degree connected by a path of length three, and the complete bipartite graph $K_{n,n+1}$ shows that this edge bound is sharp. In this paper, we obtain the above result for all $n\ge2$, and thus resolve the question of Erd\H{o}s and Hajnal completely.