It is well known that if \(G = (V, E)\) is a connected multigraph and \(X\subset V\) is a subset of even order, then G contains a spanning forest H such that each vertex from X has an odd degree in H and all the other vertices have an even degree in H. This spanning forest may have isolated vertices. If this is not allowed in H, then the situation is much more complicated. In this paper, we study this problem and generalize the concepts of even-factors and odd-factors in a unified form.

中文翻译：

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图中的特定因素

众所周知，如果\（G =（V，E）\）是连通的多重图，并且\（X \ subset V \）是偶数阶的子集，则G包含生成林H，使得X的每个顶点H的阶数为奇数，而其他所有顶点的H数为偶数。这个跨越的森林可能具有孤立的顶点。如果在H中不允许这样做，则情况要复杂得多。在本文中，我们研究了这个问题，并以统一的形式概括了偶数因子和奇数因子的概念。