Planar graphs without 4-cycles adjacent to triangles are DP-4-colorable

DOI10.1007/s00373-019-02028-zzbMath1416.05082arXiv1712.08999OpenAlexW2963733440WikidataQ128218009 ScholiaQ128218009MaRDI QIDQ2000565

Xiaowei Yu, Seog-Jin Kim

Publication date: 28 June 2019

Published in: Graphs and Combinatorics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1712.08999

zbMATH Keywords

signed graphcoloringlist coloringDP-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) Signed and weighted graphs (05C22)

Related Items (17)

Planar graphs without 7-cycles and butterflies are DP-4-colorable ⋮ A sufficient condition for planar graphs to be DP-4-colorable ⋮ A generalization of some results on list coloring and DP-coloring ⋮ Variable degeneracy on toroidal graphs ⋮ 不含带弦6-圈和项链图的平面图是DP-4-可染的 ⋮ Unnamed Item ⋮ Concepts of signed graph coloring ⋮ Every planar graph without pairwise adjacent 3-, 4-, and 5-cycle is DP-4-colorable ⋮ DP-3-coloring of planar graphs without 4, 9-cycles and cycles of two lengths from \(\{6,7,8\}\) ⋮ Combinatorial Nullstellensatz and DP-coloring of graphs ⋮ An analogue of DP-coloring for variable degeneracy and its applications ⋮ Planar graphs without cycles of lengths 4 and 5 and close triangles are DP-3-colorable ⋮ Cover and variable degeneracy ⋮ DP-\(4\)-colorability of planar graphs without intersecting \(5\)-cycles ⋮ Every planar graph without adjacent cycles of length at most 8 is 3-choosable ⋮ Relaxed DP-3-coloring of planar graphs without some cycles ⋮ DP-coloring on planar graphs without given adjacent short cycles

Cites Work

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• Correspondence coloring and its application to list-coloring planar graphs without cycles of lengths 4 to 8
• Planar graphs without 4-cycles adjacent to triangles are 4-choosable
• Choosability in signed planar graphs
• The chromatic number of a signed graph
• Signed graph coloring
• The 4-choosability of plane graphs without 4-cycles
• Every planar graph is 5-choosable
• A sufficient condition for DP-4-colorability
• A not 3-choosable planar graph without 3-cycles
• On DP-coloring of graphs and multigraphs
• DP-colorings of graphs with high chromatic number
• The asymptotic behavior of the correspondence chromatic number
• Sharp Dirac's theorem for DP‐critical graphs
• A note on a Brooks' type theorem for DP‐coloring

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