Some Results on List Total Colorings of Planar Graphs
ICCS '07 Proceedings of the 7th international conference on Computational Science, Part III: ICCS 2007
Information Processing Letters
On the total choosability of planar graphs and of sparse graphs
Information Processing Letters
Note: Total choosability of planar graphs with maximum degree 4
Discrete Applied Mathematics
Note: Total coloring of planar graphs without 6-cycles
Discrete Applied Mathematics
Information Processing Letters
Total coloring of planar graphs with maximum degree 7
Information Processing Letters
Entire colouring of plane graphs
Journal of Combinatorial Theory Series B
Total colorings of planar graphs without intersecting 5-cycles
Discrete Applied Mathematics
Survey: Randomly colouring graphs (a combinatorial view)
Computer Science Review
Total colorings of planar graphs with maximum degree 8 and without 5-cycles with two chords
Theoretical Computer Science
Total coloring of embedded graphs with maximum degree at least seven
Theoretical Computer Science
Note: Total coloring of planar graphs with 7-cycles containing at most two chords
Theoretical Computer Science
Total coloring of planar graphs with maximum degree 8
Theoretical Computer Science
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Given a graph G, a total k-coloring of G isa simultaneous coloring of the vertices and edges of G withat most k colors. If Δ(G) is the maximum degreeof G, then no graph has a total Δ-coloring, but Vizingconjectured that every graph has a total (Δ + 2)-coloring.This Total Coloring Conjecture remains open even for planar graphs.This article proves one of the two remaining planar cases, showingthat every planar (and projective) graph with Δ ≤ 7 has atotal 9-coloring by means of the discharging method. © 1999John Wiley & Sons, Inc. J Graph Theory 31: 6773, 1999