Graphs without a 3-Connected Subgraph are 4-Colourable

Édouard Bonnet; Carl Feghali; Tung Nguyen; Alex Scott; Paul Seymour; Stéphan Thomassé; Nicolas Trotignon

doi:10.37236/13181

Graphs without a 3-Connected Subgraph are 4-Colourable

Édouard Bonnet
, Carl Feghali
, Tung Nguyen
, Alex Scott
, Paul Seymour
, Stéphan Thomassé
, Nicolas Trotignon

Mathematics

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

Abstract

In 1972, Mader showed that every graph without a 3-connected subgraph is 4-degenerate and thus 5-colourable. We show that the number 5 of colours can be replaced by 4, which is best possible.

Original language	English (US)
Article number	#P1.26
Journal	Electronic Journal of Combinatorics
Volume	32
Issue number	1
DOIs	https://doi.org/10.37236/13181
State	Published - 2025

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
Geometry and Topology
Discrete Mathematics and Combinatorics
Computational Theory and Mathematics
Applied Mathematics

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10.37236/13181

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title = "Graphs without a 3-Connected Subgraph are 4-Colourable",

abstract = "In 1972, Mader showed that every graph without a 3-connected subgraph is 4-degenerate and thus 5-colourable. We show that the number 5 of colours can be replaced by 4, which is best possible.",

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AU - Bonnet, Édouard

AU - Feghali, Carl

AU - Nguyen, Tung

AU - Scott, Alex

AU - Seymour, Paul

AU - Thomassé, Stéphan

AU - Trotignon, Nicolas

PY - 2025

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AB - In 1972, Mader showed that every graph without a 3-connected subgraph is 4-degenerate and thus 5-colourable. We show that the number 5 of colours can be replaced by 4, which is best possible.

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UR - https://www.scopus.com/pages/publications/86000520379#tab=citedBy

U2 - 10.37236/13181

DO - 10.37236/13181

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JF - Electronic Journal of Combinatorics

IS - 1

M1 - #P1.26

ER -

Graphs without a 3-Connected Subgraph are 4-Colourable

Abstract

All Science Journal Classification (ASJC) codes

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