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arXiv · 1501.01079

Note on Perfect Forests

Gregory Gutin
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Abstract

A spanning subgraph $F$ of a graph $G$ is called perfect if $F$ is a forest, the degree $d_F(x)$ of each vertex $x$ in $F$ is odd, and each tree of $F$ is an induced subgraph of $G$. We provide a short proof of the following theorem of A.D. Scott (Graphs & Combin., 2001): a connected graph $G$ contains a perfect forest if and only if $G$ has an even number of vertices.

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Gregory Gutin. 2015-01-06. Note on Perfect Forests. https://arxiv.org/abs/1501.01079

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