Premium
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.
Accelerating Research
Robert Robinson Avenue,
Oxford Science Park, Oxford
OX4 4GP, United Kingdom
Address
John Eccles HouseRobert Robinson Avenue,
Oxford Science Park, Oxford
OX4 4GP, United Kingdom