Fine Structure of 4-Critical Triangle-Free Graphs I. Planar Graphs with Two Triangles and 3-Colorability of Chains

DOI10.1137/15M1023385zbMath1391.05107arXiv1505.07294OpenAlexW3100535631WikidataQ129473489 ScholiaQ129473489MaRDI QIDQ3177443

Zdeněk Dvořák, Bernard Lidický

Publication date: 25 July 2018

Published in: SIAM Journal on Discrete Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1505.07294

zbMATH Keywords

planar graphscylindercoloring

Mathematics Subject Classification ID

Planar graphs; geometric and topological aspects of graph theory (05C10) Coloring of graphs and hypergraphs (05C15)

Related Items (2)

Fine Structure of 4-Critical Triangle-Free Graphs II. Planar Triangle-Free Graphs with Two Precolored 4-Cycles ⋮ Fine Structure of 4-Critical Triangle-Free Graphs III. General Surfaces

Cites Work

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• Ore's conjecture for \(k=4\) and Grötzsch's theorem
• Planar 4-critical graphs with four triangles
• A note on the not 3-choosability of some families of planar graphs
• Grötzsch's 3-color theorem and its counterparts for the torus and the projective plane
• Three-coloring Klein bottle graphs of girth five
• Continuation of a 3-coloring from a 7-face onto a plane graph without \(C_3\)
• Grötzsch's theorem on 3-colorings
• 3-Coloring Triangle-Free Planar Graphs with a Precolored 9-Cycle
• Coloring graphs with fixed genus and girth
• Fine Structure of 4-Critical Triangle-Free Graphs III. General Surfaces
• 4-Critical Graphs on Surfaces Without Contractible $(\le\!4)$-Cycles
• Fine Structure of 4-Critical Triangle-Free Graphs II. Planar Triangle-Free Graphs with Two Precolored 4-Cycles
• On a conjecture of B. Grünbaum

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