Note on Perfect Forests

Gregory Gutin

Note on Perfect Forests

Discrete Mathematics 2015-01-07 v1

Authors: Gregory Gutin

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.

Keywords

graph theory

Cite

@article{arxiv.1501.01079,
  title  = {Note on Perfect Forests},
  author = {Gregory Gutin},
  journal= {arXiv preprint arXiv:1501.01079},
  year   = {2015}
}

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