Every planar graph without 3-cycles adjacent to 4-cycles and without 6-cycles is (1, 1, 0)-colorable

DOI10.1007/s10878-016-0039-3zbMath1369.05038OpenAlexW2409176203MaRDI QIDQ2012890

Gexin Yu, Ying Bai, Xiangwen Li

Publication date: 3 August 2017

Published in: Journal of Combinatorial Optimization (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10878-016-0039-3

zbMATH Keywords

cycleplanar graphsimproper 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)

Cites Work

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• A \((3,1)^\ast\)-choosable theorem on planar graphs
• Steinberg's conjecture is false
• Planar graphs without cycles of length 4 or 5 are (3,0,0)-colorable
• Every planar graph with cycles of length neither 4 nor 5 is \((1,1,0)\)-colorable
• Planar graphs without cycles of length from 4 to 7 are 3-colorable
• A note on the three color problem
• Structural properties of plane graphs without adjacent triangles and an application to 3-colorings
• Improper colorability of planar graphs with cycles of length neither 4 nor 6
• A Relaxation of Steinberg's Conjecture
• A note on list improper coloring planar graphs