Edge-Face Total Chromatic Number of Halin Graphs
Wai Hong Chan, Peter Che Bor Lam, Wai Chee Shiu · SIAM Journal on Discrete Mathematics · 2009
We show that the edge-face total chromatic number of Halin graphs with maximum vertex degree $\Delta$ not less than 4 is equal to $\max\{5,\Delta\}$. For the cases of $\Delta=4$ and 5, we provide a proper 5-edge-face total coloring algorithm.