Extending partial 3-colourings in a planar graph

Matt DeVos, Paul Seymour

Research output: Contribution to journalArticle

7 Scopus citations

Abstract

Let D be a disc, and let X be a finite subset of points on the boundary of D. An essential part of the proof of the four colour theorem is the fact that many sets of 4-colourings of X do not arise from the proper 4-colourings of any graph drawn in D. In contrast to this, we show that every set of 3-colourings of X arises from the proper 3-colourings of some graph drawn in D.

Original languageEnglish (US)
Pages (from-to)219-225
Number of pages7
JournalJournal of Combinatorial Theory. Series B
Volume88
Issue number2
DOIs
StatePublished - Jul 2003

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics

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