Abstract
Let $G$ be an outerplanar graph with maximum degree $\Delta(G) \ge 3$. We prove that the chromatic number $\chi(G^2)$ of the square of $G$ is at most $\Delta(G)+2$. This confirms a conjecture of Wegner [8] for outerplanar graphs. The upper bound can be further reduced to the optimal value $\Delta(G)+1$ when $\Delta(G) \ge 7$.
Citation
Ko-Wei Lih. Wei-Fan Wang. "COLORING THE SQUARE OF AN OUTERPLANAR GRAPH." Taiwanese J. Math. 10 (4) 1015 - 1023, 2006. https://doi.org/10.11650/twjm/1500403890
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