Edge-colouring eight-regular planar graphs

Maria Chudnovsky; Katherine Edwards; Paul Seymour

doi:10.1016/j.jctb.2015.05.002

Edge-colouring eight-regular planar graphs

Maria Chudnovsky, Katherine Edwards, Paul Seymour

Mathematics

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

7 Scopus citations

Abstract

It was conjectured by the third author in about 1973 that every d-regular planar graph (possibly with parallel edges) can be d-edge-coloured, provided that for every odd set X of vertices, there are at least d edges between X and its complement. For d=3 this is the four-colour theorem, and the conjecture has been proved for all d≤7, by various authors. Here we prove it for d=8.

Original language	English (US)
Pages (from-to)	303-338
Number of pages	36
Journal	Journal of Combinatorial Theory. Series B
Volume	115
DOIs	https://doi.org/10.1016/j.jctb.2015.05.002
State	Published - Nov 1 2015

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
Discrete Mathematics and Combinatorics
Computational Theory and Mathematics

Keywords

Discharging
Edge-colouring
Four-colour theorem
Planar graph
Reducible configuration

Access to Document

10.1016/j.jctb.2015.05.002

Cite this

@article{c52c86b133f047d7837fcb97473785ae,

title = "Edge-colouring eight-regular planar graphs",

abstract = "It was conjectured by the third author in about 1973 that every d-regular planar graph (possibly with parallel edges) can be d-edge-coloured, provided that for every odd set X of vertices, there are at least d edges between X and its complement. For d=3 this is the four-colour theorem, and the conjecture has been proved for all d≤7, by various authors. Here we prove it for d=8.",

keywords = "Discharging, Edge-colouring, Four-colour theorem, Planar graph, Reducible configuration",

author = "Maria Chudnovsky and Katherine Edwards and Paul Seymour",

note = "Publisher Copyright: {\textcopyright} 2015 Elsevier Inc..",

year = "2015",

month = nov,

day = "1",

doi = "10.1016/j.jctb.2015.05.002",

language = "English (US)",

volume = "115",

pages = "303--338",

journal = "Journal of Combinatorial Theory. Series B",

issn = "0095-8956",

publisher = "Academic Press Inc.",

}

TY - JOUR

T1 - Edge-colouring eight-regular planar graphs

AU - Chudnovsky, Maria

AU - Edwards, Katherine

AU - Seymour, Paul

PY - 2015/11/1

Y1 - 2015/11/1

N2 - It was conjectured by the third author in about 1973 that every d-regular planar graph (possibly with parallel edges) can be d-edge-coloured, provided that for every odd set X of vertices, there are at least d edges between X and its complement. For d=3 this is the four-colour theorem, and the conjecture has been proved for all d≤7, by various authors. Here we prove it for d=8.

AB - It was conjectured by the third author in about 1973 that every d-regular planar graph (possibly with parallel edges) can be d-edge-coloured, provided that for every odd set X of vertices, there are at least d edges between X and its complement. For d=3 this is the four-colour theorem, and the conjecture has been proved for all d≤7, by various authors. Here we prove it for d=8.

KW - Discharging

KW - Edge-colouring

KW - Four-colour theorem

KW - Planar graph

KW - Reducible configuration

UR - https://www.scopus.com/pages/publications/84939263450

UR - https://www.scopus.com/inward/citedby.url?scp=84939263450&partnerID=8YFLogxK

U2 - 10.1016/j.jctb.2015.05.002

DO - 10.1016/j.jctb.2015.05.002

M3 - Article

AN - SCOPUS:84939263450

SN - 0095-8956

VL - 115

SP - 303

EP - 338

JO - Journal of Combinatorial Theory. Series B

JF - Journal of Combinatorial Theory. Series B

ER -

Edge-colouring eight-regular planar graphs

Abstract

All Science Journal Classification (ASJC) codes

Keywords

Access to Document

Other files and links

Fingerprint

Cite this