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Note on Perfect Forests
Author(s) -
Gutin* Gregory
Publication year - 2016
Publication title -
journal of graph theory
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 54
eISSN - 1097-0118
pISSN - 0364-9024
DOI - 10.1002/jgt.21897
Subject(s) - combinatorics , mathematics , vertex (graph theory) , graph , graph factorization , perfect graph theorem , perfect graph , distance hereditary graph , discrete mathematics , factor critical graph , line graph , graph power , pathwidth
A spanning subgraph F of a graph G is called perfect if F is a forest, the degreed 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 linear‐algebraic proof of the following theorem of A. D. Scott (Graphs Combin 17 (2001), 539–553): A connected graph G contains a perfect forest if and only if G has an even number of vertices.