Plane Graphs without 4- and 5-Cycles and without Ext-Triangular 7-Cycles are 3-Colorable

DOI10.1137/16M1086418zbMath1369.05049arXiv1702.07558OpenAlexW2595530386MaRDI QIDQ5351865

Michael Schubert, Li-Gang Jin, Ying Qian Wang, Ying-Li Kang

Publication date: 31 August 2017

Published in: SIAM Journal on Discrete Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1702.07558

zbMATH Keywords

plane graphsdischargingSteinberg's conjecture3-colorability

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 (2)

\((1,0,0)\)-colorability of planar graphs without cycles of length \(4\) or \(6\) ⋮ A note on the three color problem on planar graphs without 4- and 5-cycles and without ext-triangular 7-cycles

Cites Work

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• Steinberg's conjecture is false
• Distance constraints on short cycles for 3-colorability of planar graphs
• The 3-colorability of planar graphs without cycles of length 4, 6 and 9
• An introduction to the discharging method via graph coloring
• Planar graphs without triangles adjacent to cycles of length from 4 to 7 are 3-colorable
• Planar graphs without 5- and 7-cycles and without adjacent triangles are 3-colorable
• On the 3-colorability of planar graphs without 4-, 7- and 9-cycles
• Planar graphs without cycles of length from 4 to 7 are 3-colorable
• A note on the three color problem
• Planar graphs without 4, 6, 8-cycles are 3-colorable
• Planar graphs without 4-,5- and 8-cycles are 3-colorable
• A NOTE ON 3-COLORABLE PLANE GRAPHS WITHOUT 5- AND 7-CYCLES
• Structural properties of plane graphs without adjacent triangles and an application to 3-colorings
• 没有4至6-圈的平面图是(1,0,0)-可染的

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