Let $n_1$ and $n_2$ be two integers with $n_1,n_2\ge 3$ and G a graph of order $n=n_1+n_2$. As a variation of Ore's degree condition for the existence of Hamilton cycle in G, El-Zahar proved that if $\delta (G)\ge \lceil \frac{n_1}{2}\rceil +\lceil \frac{n_2}{2}\rceil$, then G contains two disjoint cycles of length $n_1$ and $n_2$. Recently, Yan et al. considered the problem by extending the degree condition to degree sum condition and proved that if $d(u)+d(v)\ge n+4$ for any pair of non-adjacent vertices u and v of G, then G contains two disjoint cycles of length $n_1$ and $n_2$. They further asked whether the degree sum condition can be improved to $d(u)+d(v)\ge n+2$. In this paper, we give a positive answer to this question. Our result also extends El-Zahar's result when $n_1$ and $n_2$ are both odd.

让 ${ñ}_{\mathrm{1个}}$ 和 ${ñ}_2$ 是两个整数 ${ñ}_{\mathrm{1个}}，{ñ}_2\ge 3$和G的顺序图$ñ={ñ}_{\mathrm{1个}}+{ñ}_2$。El-Zahar证明了G中存在Hamilton环的Ore度条件的变化，证明了$\delta （G）\ge \lceil \frac{{ñ}_{\mathrm{1个}}}{2}\rceil +\lceil \frac{{ñ}_2}{2}\rceil$，则G包含两个长度不相交的周期${ñ}_{\mathrm{1个}}$ 和 ${ñ}_2$。最近，Yan等。通过将度数条件扩展到度数和条件来考虑问题，并证明$d（ü）+d（v）\ge ñ+4$对于任何对不相邻的顶点ù和v的ģ，然后ģ包含长度的两个不相交的周期${ñ}_{\mathrm{1个}}$ 和 ${ñ}_2$。他们进一步询问学位总和条件是否可以改善到$d（ü）+d（v）\ge ñ+2$。在本文中，我们对这个问题给出了肯定的答案。当以下情况时，我们的结果也扩展了El-Zahar的结果${ñ}_{\mathrm{1个}}$ 和 ${ñ}_2$ 都是奇怪的。