Extending partial 3-colourings in a planar graph

Matt DeVos; Paul Seymour

doi:10.1016/S0095-8956(02)00005-9

Extending partial 3-colourings in a planar graph

Matt DeVos
, Paul Seymour

Mathematics

Research output: Contribution to journal › Article › peer-review

8 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 language	English (US)
Pages (from-to)	219-225
Number of pages	7
Journal	Journal of Combinatorial Theory. Series B
Volume	88
Issue number	2
DOIs	https://doi.org/10.1016/S0095-8956(02)00005-9
State	Published - Jul 2003

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
Discrete Mathematics and Combinatorics
Computational Theory and Mathematics

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10.1016/S0095-8956(02)00005-9

Cite this

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title = "Extending partial 3-colourings in a planar graph",

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AB - 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.

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Extending partial 3-colourings in a planar graph

Abstract

All Science Journal Classification (ASJC) codes

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