On structure of some plane graphs with application to choosability

DOI10.1006/jctb.2001.2038zbMath1024.05049OpenAlexW2083028612MaRDI QIDQ1850547

Peter Che Bor Lam, Wai Chee Shiu, Bao-Gang Xu

Publication date: 10 December 2002

Published in: Journal of Combinatorial Theory. Series B (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jctb.2001.2038

zbMATH Keywords

trianglecycle

Mathematics Subject Classification ID

Paths and cycles (05C38) Planar graphs; geometric and topological aspects of graph theory (05C10) Structural characterization of families of graphs (05C75)

Related Items (18)

The Strong Fractional Choice Number and the Strong Fractional Paint Number of Graphs ⋮ Every toroidal graph without adjacent triangles is \((4,1)^{*}\)-choosable ⋮ List edge and list total colorings of planar graphs without 4-cycles ⋮ Planar graphs without intersecting 5-cycles are 4-choosable ⋮ A non-3-choosable planar graph without cycles of length 4 and 5 ⋮ Planar graphs without 7-cycles and butterflies are DP-4-colorable ⋮ 4-choosability of planar graphs with 4-cycles far apart via the Combinatorial Nullstellensatz ⋮ 不含带弦6-圈和项链图的平面图是DP-4-可染的 ⋮ On 3-choosability of plane graphs without 6-, 7- and 9-cycles ⋮ The 4-choosability of planar graphs and cycle adjacency ⋮ Planar graphs without chordal 6-cycles are 4-choosable ⋮ On 3-choosability of planar graphs without certain cycles ⋮ Bordeaux 3-color conjecture and 3-choosability ⋮ Choosability of toroidal graphs without short cycles ⋮ List coloring and diagonal coloring for plane graphs of diameter two ⋮ On 3-choosable planar graphs of girth at least 4 ⋮ A structural theorem on embedded graphs and its application to colorings ⋮ DP-coloring on planar graphs without given adjacent short cycles

Cites Work

• Some results on \((a:b)\)-choosability
• The complexity of planar graph choosability
• Colorings and orientations of graphs
• The 4-choosability of plane graphs without 4-cycles
• Every planar graph is 5-choosable
• Choosability and fractional chromatic numbers
• The list chromatic index of a bipartite multigraph
• 3-list-coloring planar graphs of girth 5
• Structural properties of plane graphs without adjacent triangles and an application to 3-colorings
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