Planar graphs without adjacent cycles of length at most five are (2, 0, 0)-colorable

DOI10.1007/s40840-020-01004-8zbMath1462.05115OpenAlexW3082304758MaRDI QIDQ2021579

Xiangwen Li, Fanyu Tian, Qin Shen

Publication date: 27 April 2021

Published in: Bulletin of the Malaysian Mathematical Sciences Society. Second Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s40840-020-01004-8

zbMATH Keywords

planar graphscoloringimproper 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) Distance in graphs (05C12)

Cites Work

• Unnamed Item
• Steinberg's conjecture is false
• Planar graphs without adjacent cycles of length at most five are \((1,1,0)\)-colorable
• Planar graphs without cycles of length 4 or 5 are \((2, 0, 0)\)-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 relaxation of the Bordeaux conjecture
• Planar graphs without triangles adjacent to cycles of length from 3 to 9 are 3-colorable
• Planar graphs with neither 5-cycles nor close 3-cycles are 3-colorable

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