A NOTE ON 3-COLORABLE PLANE GRAPHS WITHOUT 5- AND 7-CYCLES

DOI10.1142/S1793830909000270zbMath1190.05074arXiv0810.1437MaRDI QIDQ3646205

Bao-Gang Xu

Publication date: 19 November 2009

Published in: Discrete Mathematics, Algorithms and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0810.1437

zbMATH Keywords

cyclecoloringplane graph

Mathematics Subject Classification ID

Coloring of graphs and hypergraphs (05C15) Graph labelling (graceful graphs, bandwidth, etc.) (05C78)

Related Items

Plane Graphs without 4- and 5-Cycles and without Ext-Triangular 7-Cycles are 3-Colorable ⋮ The 3-colorability of planar graphs without cycles of length 4, 6 and 9 ⋮ Planar graphs with neither 5-cycles nor close 3-cycles are 3-colorable ⋮ A note on the three color problem on planar graphs without 4- and 5-cycles and without ext-triangular 7-cycles

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
• A sufficient condition for planar graphs to be 3-colorable
• Planar graphs without cycles of length from 4 to 7 are 3-colorable
• A 3-color theorem on plane graphs without 5-circuits