A proof of Wang's planar D-coloring conjecture

arXiv:2610.33322v1 Announce Type: new Abstract: We prove Wang's planar D-coloring conjecture. A D-coloring of a graph is a proper edge coloring in which every subgraph isomorphic to $K_4$ minus an edge is rainbow. Wang conjectured that every planar graph of maximum degree $\Delta$ has a D-coloring with 9 colors if $\Delta=4$, 10 colors if $\Delta=5$, and $2\Delta-1$ colors if $\Delta\ge 6$. Hu, Kong and Wang proved the cases $\Delta\le 5$ and $\Delta\ge 33$. We prove the sharp bound $2\Delta-1$ for every $\Delta\ge 6$, settling the remaining cases. The proof uses discharging; the case $\Delta=6$ is computer-assisted.

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