Three-coloring triangle-free graphs on surfaces. I: Extending a coloring to a disk with one triangle.
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Publication:290801
DOI10.1016/j.jctb.2016.04.003zbMath1337.05039arXiv1010.2472OpenAlexW2129440822WikidataQ57601328 ScholiaQ57601328MaRDI QIDQ290801
Daniel Král', Robin Thomas, Zdeněk Dvořák
Publication date: 3 June 2016
Published in: Journal of Combinatorial Theory. Series B (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1010.2472
Planar graphs; geometric and topological aspects of graph theory (05C10) Coloring of graphs and hypergraphs (05C15)
Related Items (6)
Triangle-free planar graphs with small independence number ⋮ 3-coloring triangle-free planar graphs with a precolored 9-cycle ⋮ 3-Coloring Triangle-Free Planar Graphs with a Precolored 9-Cycle ⋮ Three-coloring triangle-free graphs on surfaces. III. Graphs of girth five ⋮ Planar graphs without 4-cycles and close triangles are \((2,0,0)\)-colorable ⋮ Note on 3-choosability of planar graphs with maximum degree 4
Cites Work
- Five-coloring graphs on the Klein bottle
- Three-coloring triangle-free graphs on surfaces. II: 4-critical graphs in a disk
- On 3-colorable plane graphs without 5- and 7-cycles
- Planar graphs without 5- and 7-cycles and without adjacent triangles are 3-colorable
- The non-existence of colorings
- Every planar map is four colorable. I: Discharging
- Every planar map is four colorable. II: Reducibility
- Five-coloring graphs on the torus
- Grötzsch's 3-color theorem and its counterparts for the torus and the projective plane
- The four-colour theorem
- Color-critical graphs on a fixed surface
- The chromatic number of a graph of girth 5 on a fixed surface
- A short list color proof of Grötzsch's theorem
- Three-coloring Klein bottle graphs of girth five
- 3-list-coloring planar graphs of girth 5
- Grötzsch's theorem on 3-colorings
- Three-coloring triangle-free planar graphs in linear time
- Every Planar Map is Four Colorable
- Coloring graphs with fixed genus and girth
- 4-chromatic projective graphs
- 6-Critical Graphs on the Klein Bottle
- On a conjecture of B. Grünbaum
- Map-Colour Theorems
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