In this paper, we consider a general degree sum condition sufficient to imply the existence of k vertex-disjoint chorded cycles in a graph G. Let \(\sigma _t(G)\) be the minimum degree sum of t independent vertices of G. We prove that if G is a graph of sufficiently large order and \(\sigma _t(G)\ge 3kt-t+1\) with \(k\ge 1\), then G contains k vertex-disjoint chorded cycles. We also show that the degree sum condition on \(\sigma _t(G)\) is sharp. To do this, we also investigate graphs without chorded cycles.

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关于度和条件和顶点不相交的弦周期

在本文中，我们考虑了一个一般的度数求和条件，足以暗示图G中存在k个顶点不相交的和弦循环。让\（\西格玛_t（G）\）是度最小总和吨的独立顶点ģ。我们证明，如果G是足够大的阶且\（\ sigma _t（G）\ ge 3kt-t + 1 \）与\（k \ ge 1 \）的图，则G包含k个顶点不相交的弦周期。我们还表明，\（\ sigma _t（G）\）上的度和条件很尖锐。为此，我们还研究了没有弦周期的图。