Bujtás, Csilla ; Jendrol', Stanislav ; Tuza, Zsolt
It is well known that if ▫$G = (V, E)$▫ is a 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.
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