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Folding = Colouring

2008/02/18 by David R. Wood, Wood, David R. · 1 citation
Computer Science · Engineering · Mathematics · #05C15 #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Graph Labeling and Dimension Problems #graph theory and CDMA systems #math.CO #msc:05C15

paper · pdf · doi:10.48550/arxiv.0802.2467

I have discovered that the main result was first proved by Cook and Evans in 1979

openalex publication_date 2008/02/18 · arxiv created 2008/02/25 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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