Geodesic
Total colorings of \(F_5\)-free planar graphs with maximum degree 8
The electronic journal of combinatorics, Tome 21 (2014) no. 1
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The total chromatic number of a graph $G$, denoted by $\chi′′(G)$, is the minimum number of colors needed to color the vertices and edges of $G$ such that no two adjacent or incident elements get the same color. It is known that if a planar graph $G$ has maximum degree $\Delta ≥ 9$, then $\chi′′(G) = \Delta + 1$. The join $K_1 \vee P_n$ of $K_1$ and $P_n$ is called a fan graph $F_n$. In this paper, we prove that if $G$ is a $F_5$-free planar graph with maximum degree 8, then $\chi′′(G) = 9$.
DOI : 10.37236/3303
Classification : 05C15, 05C10, 05C07, 05C35
Mots-clés : planar graph, total coloring, cycle 
@article{10_37236_3303,
     author = {Jian Chang and Jian-Liang Wu and Hui-Juan Wang and Zhan-Hai Guo},
     title = {Total colorings of {\(F_5\)-free} planar graphs with maximum degree 8},
     journal = {The electronic journal of combinatorics},
     year = {2014},
     volume = {21},
     number = {1},
     doi = {10.37236/3303},
     zbl = {1300.05092},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/3303/}
}
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Jian Chang; Jian-Liang Wu; Hui-Juan Wang; Zhan-Hai Guo. Total colorings of \(F_5\)-free planar graphs with maximum degree 8. The electronic journal of combinatorics, Tome 21 (2014) no. 1. doi: 10.37236/3303

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