Total colorings of planar graphs with large maximum degree
Journal of Graph Theory
Total colourings of planar graphs with large girth
European Journal of Combinatorics
Graph Theory With Applications
Graph Theory With Applications
On total 9-coloring planar graphs of maximum degree seven
Journal of Graph Theory
Total-Coloring of Plane Graphs with Maximum Degree Nine
SIAM Journal on Discrete Mathematics
Planar graphs with maximum degree 8 and without adjacent triangles are 9-totally-colorable
Discrete Applied Mathematics
On the 7 Total Colorability of Planar Graphs with Maximum Degree 6 and without 4-cycles
Graphs and Combinatorics
Note: Total coloring of planar graphs without 6-cycles
Discrete Applied Mathematics
Local condition for planar graphs of maximum degree 7 to be 8-totally colorable
Discrete Applied Mathematics
Total coloring of planar graphs with maximum degree 7
Information Processing Letters
Total colorings of planar graphs with maximum degree 8 and without 5-cycles with two chords
Theoretical Computer Science
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A total k-coloring of a graph G is a coloring of V(G)@?E(G) using k colors such that no two adjacent or incident elements receive the same color. The total chromatic number of G is the smallest integer k such that G has a total k-coloring. In this paper, it is proved that if G is a planar graph with maximum degree @D=7 and without intersecting 5-cycles, that is, every vertex is incident with at most one cycle of length 5, then the total chromatic number of G is @D+1.