Folding = Colouring
Abstract
The foldings of a connected graph $G$ are defined as follows. First, $G$ is a folding of itself. Let $G'$ be a graph obtained from $G$ by identifying two vertices at distance 2 in $G$. Then every folding of $G'$ is a folding of $G$. The folding number of $G$ is the minimum order of a complete folding of $G$. Theorem: The folding number of every graph equals its chromatic number.
 Publication:

arXiv eprints
 Pub Date:
 February 2008
 DOI:
 10.48550/arXiv.0802.2467
 arXiv:
 arXiv:0802.2467
 Bibcode:
 2008arXiv0802.2467W
 Keywords:

 Mathematics  Combinatorics;
 05C15
 EPrint:
 I have discovered that the main result was first proved by Cook and Evans in 1979