Every planar graph without cycles of lengths 4 to 12 is acyclically 3-choosable

DOI10.1016/j.ipl.2009.08.004zbMath1197.05050OpenAlexW1966005013MaRDI QIDQ990957

Hervé Hocquard, Mickaël Montassier

Publication date: 1 September 2010

Published in: Information Processing Letters (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.ipl.2009.08.004

zbMATH Keywords

planar graphscombinatorial problemsforbidden cyclesacyclic choosability

Mathematics Subject Classification ID

Planar graphs; geometric and topological aspects of graph theory (05C10) Coloring of graphs and hypergraphs (05C15) Graph labelling (graceful graphs, bandwidth, etc.) (05C78)

Related Items (9)

Acyclic 5-choosability of planar graphs without adjacent short cycles ⋮ Acyclic 4-choosability of planar graphs ⋮ Planar graphs without 4- and 5-cycles are acyclically 4-choosable ⋮ Acyclic 5-choosability of planar graphs without 4-cycles ⋮ Acyclic 4‐Choosability of Planar Graphs with No 4‐ and 5‐Cycles ⋮ A note on the acyclic 3-choosability of some planar graphs ⋮ Acyclic 3-choosability of sparse graphs with girth at least 7 ⋮ Acyclic 4-choosability of planar graphs with neither 4-cycles nor triangular 6-cycles ⋮ Acyclic 4-choosability of planar graphs without adjacent short cycles

Cites Work

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• Planar graphs without cycles of length from 4 to 7 are 3-colorable
• Acyclic list 7‐coloring of planar graphs
• Structural properties of plane graphs without adjacent triangles and an application to 3-colorings
• On the acyclic choosability of graphs
• Acyclic 5-choosability of planar graphs without 4-cycles
• 25 pretty graph colouring problems

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