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Let $G$ be a graph and let $g$, $f$, and $f'$ be three positiveinteger-valued functions on $V(G)$ with $g\le f$. Tokuda, Xu, and Wang (2003)showed that if $G$ contains a $(g,f)$-factor and a spanning $f'$-tree, then $G$also contains a connected $(g,f+f'-1)$-factor. In this note, we develop theirresult to a tree-connected version by proving that if $G$ contains a$(g,f)$-factor and an $m$-tree-connected $(m,f')$-factor, then $G$ alsocontains an $m$-tree-connected $(g,f+f'-m)$-factor, provided that $f\ge m$. Inaddition, we show that $g$ allows to be nonnegative.

The existence of $m$-tree-connected $(g,f+f'-m)$-factors using $(g,f)$-factors and $m$-tree-connected $(m,f')$-factors