Triangle-free graphs that do not contain an induced subdivision of K4 are 3-colorable

Maria Chudnovsky; Chun Hung Liu; Oliver Schaudt; Sophie Spirkl; Nicolas Trotignon; Kristina Vušković

doi:10.1002/jgt.22441

Triangle-free graphs that do not contain an induced subdivision of K₄ are 3-colorable

Maria Chudnovsky
, Chun Hung Liu
, Oliver Schaudt
, Sophie Spirkl
, Nicolas Trotignon
, Kristina Vušković

Mathematics

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

5 Scopus citations

Abstract

We show that triangle-free graphs that do not contain an induced subgraph isomorphic to a subdivision of K₄ are 3-colorable. This proves a conjecture of Trotignon and Vušković [J. Graph Theory. 84 (2017), no. 3, pp. 233–248].

Original language	English (US)
Pages (from-to)	67-95
Number of pages	29
Journal	Journal of Graph Theory
Volume	92
Issue number	2
DOIs	https://doi.org/10.1002/jgt.22441
State	Published - Oct 2019

All Science Journal Classification (ASJC) codes

Geometry and Topology
Discrete Mathematics and Combinatorics

Keywords

coloring
induced subgraph

Access to Document

10.1002/jgt.22441

Cite this

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title = "Triangle-free graphs that do not contain an induced subdivision of K4 are 3-colorable",

abstract = "We show that triangle-free graphs that do not contain an induced subgraph isomorphic to a subdivision of K4 are 3-colorable. This proves a conjecture of Trotignon and Vu{\v s}kovi{\'c} [J. Graph Theory. 84 (2017), no. 3, pp. 233–248].",

keywords = "coloring, induced subgraph",

author = "Maria Chudnovsky and Liu, \{Chun Hung\} and Oliver Schaudt and Sophie Spirkl and Nicolas Trotignon and Kristina Vu{\v s}kovi{\'c}",

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AU - Chudnovsky, Maria

AU - Liu, Chun Hung

AU - Schaudt, Oliver

AU - Spirkl, Sophie

AU - Trotignon, Nicolas

AU - Vušković, Kristina

PY - 2019/10

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AB - We show that triangle-free graphs that do not contain an induced subgraph isomorphic to a subdivision of K4 are 3-colorable. This proves a conjecture of Trotignon and Vušković [J. Graph Theory. 84 (2017), no. 3, pp. 233–248].

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KW - induced subgraph

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