Year: 2026
Type: preprint
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 $Δ$ has a $D$-coloring with $9$ colors if $Δ=4$, $10$ colors if $Δ=5$, and $2Δ-1$ colors if $Δ\ge6$. Hu, Kong and Wang proved the cases $Δ\le5$ and $Δ\ge33$. We prove the sharp bound $2Δ-1$ for every $Δ\ge6$, settling the remaining cases. The proof uses discharging; the case $Δ=6$ is computer-assisted.
Source: arXiv (Cornell University)
Author: Verma, Harshit
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7223992147