Planar graphs without triangles adjacent to cycles of length from 4 to 7 are 3-colorable

DOI10.1016/j.disc.2010.03.021zbMath1203.05048OpenAlexW2095074152MaRDI QIDQ709301

Oleg V. Borodin, Andre Raspaud, Alekseĭ Nikolaevich Glebov

Publication date: 18 October 2010

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

Full work available at URL: https://doi.org/10.1016/j.disc.2010.03.021

zbMATH Keywords

graphplanar graph3-coloring

Mathematics Subject Classification ID

Coloring of graphs and hypergraphs (05C15)

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Steinberg's conjecture is false ⋮ Every planar graph without triangles adjacent to cycles of length 3 or 6 is \(( 1 , 1 , 1 )\)-colorable ⋮ A step towards the strong version of Havel's three color conjecture ⋮ Plane Graphs without 4- and 5-Cycles and without Ext-Triangular 7-Cycles are 3-Colorable ⋮ Short proofs of coloring theorems on planar graphs ⋮ Planar graphs with cycles of length neither 4 nor 6 are \((2,0,0)\)-colorable ⋮ Distance constraints on short cycles for 3-colorability of planar graphs ⋮ \((1,0,0)\)-colorability of planar graphs without prescribed short cycles ⋮ The 3-colorability of planar graphs without cycles of length 4, 6 and 9 ⋮ Decomposing a planar graph without triangular 4-cycles into a matching and a 3-colorable graph ⋮ A refinement of choosability of graphs ⋮ Planar graphs without adjacent cycles of length at most five are \((1,1,0)\)-colorable ⋮ A relaxation of Novosibirsk 3-color conjecture ⋮ Planar graphs without short even cycles are near-bipartite

Cites Work

• On 3-colorable plane graphs without 5- and 7-cycles
• Planar graphs without 5- and 7-cycles and without adjacent triangles are 3-colorable
• Planar graphs without adjacent cycles of length at most seven are 3-colorable
• A sufficient condition for planar graphs to be 3-colorable
• Planar graphs without cycles of length from 4 to 7 are 3-colorable
• A note on the three color problem
• Planar graphs without triangles adjacent to cycles of length from 3 to 9 are 3-colorable
• Continuation of a 3-coloring from a 7-face onto a plane graph without \(C_3\)
• A 3-color theorem on plane graphs without 5-circuits
• Coloring graphs with fixed genus and girth
• The color space of a graph
• Structural properties of plane graphs without adjacent triangles and an application to 3-colorings
• On a conjecture of B. Grünbaum
• 25 pretty graph colouring problems
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