Planar graphs without 4- and 5-cycles are acyclically 4-choosable

DOI10.1016/j.dam.2012.11.006zbMath1262.05029OpenAlexW2087399690MaRDI QIDQ1949098

Min Chen, Andre Raspaud

Publication date: 25 April 2013

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

Full work available at URL: https://doi.org/10.1016/j.dam.2012.11.006

zbMATH Keywords

cycleplanar graphschoosabilityacyclic coloring

Mathematics Subject Classification ID

Paths and cycles (05C38) Planar graphs; geometric and topological aspects of graph theory (05C10) Coloring of graphs and hypergraphs (05C15)

Related Items (10)

Construction of acyclically 4-colourable planar triangulations with minimum degree 4 ⋮ Acyclic coloring of graphs without bichromatic long path ⋮ An improved upper bound for the acyclic chromatic number of 1-planar graphs ⋮ Acyclic 4-choosability of planar graphs without intersecting short cycles ⋮ Acyclic 4-choosability of planar graphs without 4-cycles ⋮ An introduction to the discharging method via graph coloring ⋮ Equitable partition of planar graphs ⋮ On acyclic 4-choosability of planar graphs without cycles of length 4, 7 and 9 ⋮ Unnamed Item ⋮ Acyclic 6-choosability of planar graphs without 5-cycles and adjacent 4-cycles

Cites Work

• Acyclic 4-choosability of 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
• A non-3-choosable planar graph without cycles of length 4 and 5
• Acyclic 3-choosability of planar graphs with no cycles of length from 4 to 11
• On acyclic 4-choosability of planar graphs without short cycles
• Every planar graph without cycles of lengths 4 to 12 is acyclically 3-choosable
• Acyclic 5-choosability of planar graphs with neither 4-cycles nor chordal 6-cycles
• Note to the paper of Grünbaum on acyclic colorings
• Every planar graph has an acyclic 7-coloring
• On acyclic colorings of planar graphs
• Every planar graph is 5-choosable
• Every planar graph has an acyclic 8-coloring
• A sufficient condition for planar graphs to be acyclically 5-choosable
• Acyclic 5-choosability of planar graphs without adjacent short cycles
• Acyclic 5-choosability of planar graphs without small cycles
• Planar graphs without 4-cycles are acyclically 6-choosable
• Acyclic Colourings of Planar Graphs with Large Girth
• Acyclic list 7‐coloring of planar graphs
• On the acyclic choosability of graphs
• Acyclic 5-choosability of planar graphs without 4-cycles
• Acyclic 5-choosability of planar graphs without 4-cycles
• Acyclic colorings of planar graphs
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