Let G be a tripartite graph with tripartition \((V_{1},V_{2},V_{3})\), where \(\mid V_{1}\mid =\mid V_{2}\mid =\mid V_{3}\mid =k>0\). It is proved that if \(d(x)+d(y)\ge 3k\) for every pair of nonadjacent vertices \(x\in V_{i}, y\in V_{j}\) with \(i\ne j(i,j\in \{1,2,3\})\), then G contains k vertex-disjoint triangles. As a corollary, if \(d(x)\ge \frac{3}{2}k\) for each vertex \(x\in V(G)\), then G contains k vertex-disjoint triangles. Based on the above results, vertex-disjoint triangles in multigraphs are studied. Let M be a standard tripartite multigraph with tripartition \((V_{1},V_{2},V_{3})\), where \(\mid V_{1} \mid =\mid V_{2}\mid =\mid V_{3} \mid =k>0\). If \(\delta (M)\ge 3k-1\) for even k and \(\delta (M)\ge 3k\) for odd k, then M contains k vertex-disjoint 4-triangles \(\varDelta _{4}\)(a triangle with at least four edges). Furthermore, examples are given showing that the degree conditions of all our three results are best possible.

令G为具有三重\（（V_ {1}，V_ {2}，V_ {3}）\）的三方图，其中\（\ mid V_ {1} \ mid = \ mid V_ {2} \ mid = \ mid V_ {3} \ mid = k> 0 \）。它证明了当\（d（X）+ d（Y）\ GE 3K \）对于每对不相邻顶点的\（X \在V_ {I}，Y \在V_ {Ĵ} \）与\（ⅰ \ ne j（i，j \ in \ {1,2,3 \}）\），则G包含k个顶点不相交的三角形。作为推论，如果对于每个顶点\（d（x）\ ge \ frac {3} {2} k \）\（x \ in V（G）\），则G包含k个顶点不相交的三角形。基于以上结果，研究了多图中顶点不相交的三角形。让M是具有三方\（（V_ {1}，V_ {2}，V_ {3}）\）的标准三方多重图，其中\（\ mid V_ {1} \ mid = \ mid V_ {2} \ mid = \ mid V_ {3} \ mid = k> 0 \）。如果\（\增量（M）\ GE 3K-1 \）为偶数ķ和\（\增量（M）\ GE 3K \）对于奇数ķ，然后中号包含ķ顶点不相交4-三角形\（\ varDelta _ {4} \）（至少四个边的三角形）。此外，给出的示例表明，我们所有三个结果的程度条件都是最可能的。