Preprint
Aug 2026
On B-Colorings in Planar Graphs
Gy\'arf\'as and S\'ark\"ozy [Studia Sci. Math. Hungar., 2023] defined a B-coloring of a graph to be a proper coloring of the edge set in which any $C_4$ is totally multicolored. Let $q_B(G)$ denote the minimum number of colors sufficient for a B-coloring of a graph $G$. In this paper, we prove that any planar graph $G$ with $\Delta=\Delta(G)$ and $\Delta_2=\Delta_2(G)$ has $q_B(G)\leq\Delta+\max\{\Delta_2,38\}$, refining a bound by Kong, Wang, and Zheng [J. Graph Theory, 2026].
Anthony Vuolo
· 2 citations