Total colorings of planar graphs with maximum degree at least 8

DOI10.1007/S11425-008-0155-3zbMath1190.05073OpenAlexW2355967809MaRDI QIDQ1043002

Lan Shen, Ying Qian Wang

Publication date: 7 December 2009

Published in: Science in China. Series A (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11425-008-0155-3

zbMATH Keywords

cycleplanar graphchordtotal coloringmaximum degree

Mathematics Subject Classification ID

Graph theory (including graph drawing) in computer science (68R10) Coloring of graphs and hypergraphs (05C15)

Related Items (19)

Total colorings of embedded graphs with no 3-cycles adjacent to 4-cycles ⋮ Total coloring of planar graphs without adjacent chordal 6-cycles ⋮ Total coloring of planar graphs without 6-cycles ⋮ Planar graphs with maximum degree 8 and without intersecting chordal 4-cycles are 9-totally colorable ⋮ \((\Delta + 1)\)-total-colorability of plane graphs with maximum degree \(\Delta\) at least 6 and without adjacent short cycles ⋮ Total coloring of planar graphs without some adjacent cycles ⋮ \((\Delta +1)\)-total-colorability of plane graphs of maximum degree \(\Delta\geq 6\) with neither chordal \(5\)-cycle nor chordal \(6\)-cycle ⋮ Total coloring of planar graphs with maximum degree \(7\) ⋮ A note on the total coloring of planar graphs without adjacent 4-cycles ⋮ Minimum total coloring of planar graphs with maximum degree 8 ⋮ Total colorings of planar graphs without intersecting 5-cycles ⋮ Total colorings of planar graphs without chordal 6-cycles ⋮ Minimum total coloring of planar graph ⋮ A sufficient condition for planar graphs with maximum degree 8 to be 9-totally colorable ⋮ Total coloring of planar graphs without chordal short cycles ⋮ Total coloring of planar graphs without adjacent short cycles ⋮ Local condition for planar graphs of maximum degree 7 to be 8-totally colorable ⋮ Planar graphs with maximum degree 7 and without 5-cycles are 8-totally-colorable ⋮ Total coloring of planar graphs without some chordal 6-cycles

Cites Work

• List edge and list total colorings of planar graphs without 4-cycles
• Total colorings of planar graphs without small cycles
• Total colourings of planar graphs with large girth
• On total chromatic number of planar graphs without 4-cycles
• Total chromatic number of planar graphs with maximum degree ten
• Total-Coloring of Plane Graphs with Maximum Degree Nine
• Total colorings of planar graphs with large maximum degree
• SOME UNSOLVED PROBLEMS IN GRAPH THEORY

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